text:
\section{Introduction}

In the beginning of  the development of inflationary cosmology our main goal was to find some simple semi-realistic versions of inflationary theory, where inflation could be naturally realized for a wide variety of initial conditions. The search for such models has lead us to the discovery of chaotic inflation \cite{Chaot}, where inflation can be achieved in the simplest models, such as the models of the fields minimally coupled to gravity, with polynomial potentials. Inflation occurs in such models for a wide variety of initial conditions \cite{Linde:1985ub} and may continue eternally \cite{Vilenkin:1983xq,Linde:1986fd}.

In this class of theories the constant part of the scalar field does not have any independent physical meaning; its value enters the theory only because it makes other fields massive, and because it has a potential energy density $V(\varphi)$. As a result, these theories have a weakly broken shift symmetry $\varphi \to \varphi+c$. This is broken only by the $\varphi$-dependence of the potential $V$ and of the masses of particles interacting with the field $\varphi$. It is this property which allows the existence of chaotic inflation potentials such as $m^{2}\varphi^{2}$, which remain flat even for $\varphi \gg M_{p}$ \cite{Chaot}. Shift symmetries forbid the dangerous quantum corrections to the effective potential $\sim M_p^{4} \bigl(\frac{\varphi}{M_{p}}\bigr)^{n}$ often discussed in the literature which renders inflation in these theories easier to achieve;  see \cite{Linde:2007fr} for a recent discussion of this issue. Another popular example of shift symmetry is the symmetry $\theta \to \theta + c$ of the axion potential; this potential appears only after the shift symmetry becomes broken by non-perturbative effects. This symmetry was the basis for the so-called natural inflation scenario \cite{Freese:1990rb}.

However, in supergravity and string theory the scalar fields usually have physical or geometric meaning. For example, in the simplest supergravity models the K\"ahler potential $K = \frac{\Phi\bar\Phi}{M_p^{2}}$ describes K\"ahler geometry. The F-term scalar potential is proportional to $e^{K} \sim e^{\Phi\bar\Phi/ M_p^{2}}$. As a result, the mass of the inflaton field typically acquires a contribution $O(H^{2})$, which tends to prevent inflation. Quite often, one can fine tune the parameters of the theory and achieve desirable flatness of the potential for some small range of the values of the scalar fields. In such models, inflation in a certain sense happens by accident: One must have the parameters of the models fixed in a very narrow range, and in addition, one should hope that the scalar field from the very beginning by some happy accident was in the required range of its values where inflation is possible. A similar situation, which can be called `accidental inflation,' often occurs in string theory.

An interesting and quite instructive model of this type was proposed by Holman,  Ramond and Ross \cite{Holman:1984yj}. We will briefly describe it here, because it will be closely related to the models of string theory inflation to be discussed in this paper.
The  K\"ahler potential in this model is $K = \frac{\Phi\bar\Phi}{M_p^{2}}$, and the superpotential  is
\begin{equation}
W = c\, (\Phi-\Phi_{0})^{2}\ ,
\end{equation}
where $\Phi = (\varphi +i\alpha)/\sqrt 2$, and $\varphi$ and $\alpha$ are canonically normalized scalar fields. The potential has a minimum at $\alpha = 0$, $\varphi = \sqrt 2 \Phi_{0}$.

In what follows, we will work in units $M_{p} = 1$. For the particular case $\Phi_{0}  = 1$, the potential $V(\varphi)$ is shown by the thick blue solid line in Fig. 1. It has a minimum at $\varphi = \sqrt 2$, and a small plateau at $|\varphi| \ll 1$, where the potential is described by the simple equation
\begin{equation}\label{cubic}
V(\varphi) =V_{0}\, (1-\sqrt 2\, \varphi^{3} + O(1)\,\varphi^{4}) \ ,
\end{equation}
where $V_{0} = c^{2}$.

\begin{figure}
\centering{\includegraphics[height=5cm]{Ramond.eps}}
 \caption{The thick blue solid line shows the inflationary potential for the model of Ref. \cite{Holman:1984yj}, with $\Phi_{0} = 1$.  If one takes the model with a slightly larger $\Phi_{0}$, the potential has two minima separated by a barrier, as shown by the thin green dashed line, corresponding to $\Phi_{0} = 1.05$. For  $\Phi_{0}<1$, the metastable minimum disappears, and $V'$ becomes negative everywhere, as shown by the thin red solid line corresponding to $\Phi_{0} = 0.95$. Inflation is possible only if $|\Phi_{0}-1|\ll 1$, which requires fine tuning.} \label{Ramond}
\end{figure}

This potential is flat   at $\varphi = 0$, $V' = V'' = 0$, which corresponds to an inflection point. Since the slow-roll parameters $\epsilon$ and $\eta $ vanish at $\varphi = 0$, this potential can support inflation if the initial value of the field is sufficiently small. The slow-roll conditions in this model are satisfied for $\varphi \lesssim 10^{{-1}}$. The field $\varphi_{60}$ corresponding to the beginning of the period of the last 60 e-foldings is even much smaller. Therefore it is quite sufficient to use just  the first two terms of the expression (\ref{cubic}), i.e. the constant and the cubic term, for investigation of inflation in this model.

On the other hand, there is no special reason why $\Phi_{0}$ must be exactly equal $1$. If we take, for example, $\Phi_{0}= 0.95$, we will obtain a steep potential shown by the thin red solid line in Fig. 1, and inflation disappears. For   $\Phi_{0}= 1.05$, the potential has two minima and a non-inflationary maximum with $V'' \sim V$. To achieve 60 e-folds of inflation in this scenario one must have $\Phi = 1$ with a great accuracy, and the universe from the very beginning should reside very close to the inflection point $\varphi = 0$. In this sense, inflation happens in the models of this type by accident.

This model was proposed  back in 1984. It took 10 years, from 1984 to 1994, until the hybrid inflation scenario was developed \cite{Hybrid} and it became possible to introduce the F-term \cite{F} and the D-term hybrid inflation scenario \cite{D}, where inflation could appear in a relatively natural way. It took 6 more years after that until the simple realization of  chaotic inflation with a quadratic potential was proposed in supergravity  \cite{Kawasaki:2000yn}, and it took 7 more years until a supergravity realization of natural inflation became possible \cite{Kallosh:2007ig}.

A systematic investigation of inflation in string theory began only in 2003, after the development of the KKLT mechanism of vacuum stabilization \cite{KKLT}, see also \cite{Giddings:2001yu,Silverstein:2001xn}. The first string inflation model based on the KKLT mechanism, the KKLMMT model  \cite{Kachru:2003sx}, is a brane inflation version of the hybrid inflation scenario. A detailed investigation of this model \cite{Baumann:2007np,delicate,Krause:2007jk,Panda:2007ie,Itzhaki:2007nk}
 demonstrated that its inflationary potential is very similar to the inflection point potential of Ref.  \cite{Holman:1984yj}.\footnote{Similar potentials emerge in other inflationary models as well, such as the MSSM inflation, see  Ref. \cite{Allahverdi:2006we}.}  Thus, in a certain sense, in the recent studies of string theory inflation we returned to the discussion of accidental inflation in the first models of inflation in supergravity.

In parallel with the investigation of the KKLMMT scenario, string theorists are trying to develop more natural versions of inflationary theory, where the inflationary potential would naturally have flat directions, such as D3/D7 inflation \cite{D3D7}. We do not know yet whether it is possible to obtain a generalization of the chaotic inflation scenario and/or of the natural inflation scenario; some related ideas are discussed e.g. in \cite{Dimopoulos:2005ac,Kallosh:2007ig,McAllister:2007bg,Grimm:2007hs}. As we just mentioned, the search for such models in supergravity took many years. The investigation of inflation in string theory has just began. Therefore at this early stage it may make a lot of sense to study the models of accidental inflation discussed above, despite the fact that they appear fine-tuned in more than one respect. This may be quite appropriate because the old ideas of naturalness, unnaturalness and fine-tuning look quite different in the context of the eternal inflation scenario in the string theory landscape consisting of $10^{10^{3}}$ different string theory vacua \cite{Lerche,Bousso,KKLT,Susskind:2003kw, Douglas:2003um}.

In this paper we will pursue two different goals. First of all,  the  dynamical mechanism of inflation in the KKLMMT model is quite complicated. It involves investigation of gravitational effects related to the motion of branes in warped space, which requires a consistent merger of open string theory and closed string theory. Therefore it would be nice to have a simple  toy model of accidental inflation in string theory, analogous to the model of Ref. \cite{Holman:1984yj}.  An example of such model will be presented in Section \ref{KLinf}.

Secondly, we would like to understand generic features of accidental inflation in the context of the string landscape scenario,  and, if possible, to find some unambiguous predictions of this class of models which would allow us to distinguish it from other versions of string inflation. These issues will be discussed in Sections  \ref{toyinf} -- \ref{predict}. We will summarize our results in Section \ref{concl}. A short discussion concerning eternal inflation can be found in the Appendix.

\section{Volume modulus inflation}\label{KLinf}

For a long time, it did not seem possible that the volume modulus may play the role of the inflaton field in the KKLT construction. Indeed, the standard KKLT potential has only one minimum at finite values of the volume modulus, and the slow-roll conditions for this potential are strongly violated~\cite{alphaprime}.

The situation did not change much with the invention of the racetrack inflation: It became possible to find a saddle point of the potential and satisfy the slow-roll conditions  with respect to the axion field, but not with respect to  the volume modulus \cite{Blanco-Pillado:2004ns}.

In this section, we propose a model of string theory inflation driven by the volume modulus in the context of the KL~\cite{Kallosh:2004yh} model of moduli stabilization. (Another model of the volume modulus inflation will be described soon  in \cite{CKLQ}.) Here the combination of fluxes with a racetrack superpotential leads to a scalar potential with two local asymmetric minima for the volume modulus which become de Sitter after uplifting by e.g. $\overline{\rm D3}$-branes or ${\rm D7}$-induced D-terms. The higher of the two minima connects through a saddle point to the late-time dS minimum, or degenerates into an inflection point. With a proper choice of parameters, one can make the potential near the saddle point or the inflection point  sufficiently flat to provide for
more than the necessary 60 e-foldings of slow-roll inflation driven by the volume modulus.

To begin with, we shall thus shortly review the structure of the KL setup~\cite{Kallosh:2004yh}. The model starts out similar to the KKLT construction~\cite{KKLT} by assuming that the complex structure moduli and the axion-dilaton have been frozen at a high KK-related mass scale by turning on sufficiently generic 3-form fluxes $G_3$ along the lines of~\cite{Giddings:2001yu}. With respect to the K\"ahler moduli this results in a constant and fine-tunable term $W_0=\int_{\rm CY_3}G_3\wedge \Omega$ in superpotential of the low-energy effective 4d ${\cal N}=1$ supergravity. Considering then the subclass of Calabi-Yau 3-folds with $h^{1,1}=1$, i.e. a single K\"ahler modulus which is the volume modulus $T$, the presence of non-perturbative effects leads to the stabilization of $T$. These exponential terms
arise  either from Euclidean ${\rm D3}$-branes of from gaugino condensation  on ${\rm D7}$-branes, as explained in
\cite{KKLT,Blanco-Pillado:2004ns}. If there is only one exponential term in the superpotential, then this leads directly to the KKLT construction.

The KL model is then specified by assuming the presence of non-perturbative contributions in $T$ to the superpotential, leading to a racetrack superpotential. Thus the setup is given by
\begin{eqnarray}
K &=& - 3 \ln(T + \overline{T})\;,\qquad T=\varphi+i\tau \ , \nonumber\\ &&\\
W &=& W_0 + Ae^{-aT}+ Be^{-bT} \ ,\nonumber
\label{setup}
\end{eqnarray}
where the volume modulus $\varphi$ measuring the volume of the single 4-cycle of the Calabi-Yau pairs up with the RR-axion $\tau$ to form the complex chiral superfield $T$.

The F-term scalar potential, \begin{equation} V= e^{K}\left(  G^{T \overline T} D_{T}W \overline {D_{T} W}
- 3|W|^2 \right), \end{equation} as the function of the volume modulus $\varphi$ is given by
\begin{eqnarray}
&&V= \frac{e^{-2(a+b)\varphi}}{6\varphi^2}(b B e^{a\varphi}+ a A e^{b\varphi})\nonumber
\\ &\times& \left [Be^{a\varphi}(3+b\varphi)+e^{b\varphi}(A(3+a\varphi)+3e^{a\varphi}W_0)\right].
\label{pot}\end{eqnarray}
It can be shown that this is a minimum in the axion direction, provided we take we take  $A,a$, $B, b$ and $W_0$ to be  all real
and the sign of $A$ and $B$ opposite, as well as $a>b$ and $A>|B|$.

Up to this point, the KL model does not differ from other racetrack models. However, as it was found in \cite{Kallosh:2004yh},  the scalar potential in this model for some values of its parameters has  {\it two} supersymmetric AdS minima which solve $D_T W=0$. The one at smaller volume is given (similarly to the heterotic racetrack models) by
\begin{equation}
 \varphi_{cr}= \frac{1}{a-b}\ln \left |\frac{a\,A}{b\,B}\right| \ ,
\label{ReTcr} \end{equation}
while the one at larger volume is the deeper AdS minimum of the two with its position determined similarly to the KKLT case
\begin{equation}
\varphi_{_{\rm KKLT-like}}\sim-\frac{1}{a}\ln(W_0/A)\;.\label{ReTAdS}
\end{equation}
In the special case where one arranges for a particular relation
between the  parameters of the superpotential,
\begin{equation} -W_0= A \left |\frac{a\,A}{
b\,B}\right|^\frac{a}{b-a} +B \left |\frac{a\,A}{b\,B}\right| ^\frac{b}{b-a}\ , \end{equation}
the smaller volume `racetrack-like' minimum actually becomes a SUSY Minkowski one with vanishing gravitino mass~\cite{Kallosh:2004yh}.

\begin{figure}
\centering{\hskip 1cm ~ \includegraphics[height=5cm]{1dpot.eps}}
 \caption{The uplifted potential for $W_0= 4\cdot 10^{-8},\ A=1,\ B=-0.62704017319,\ a=2\pi/58,\
b=2\pi/60,\ C=3.01\cdot 10^{-18}$. The potential is shown in units of $10^{{-23}}$ of the Planck density. A late-time dS minimum at $V\approx 0$ stabilizes the volume at $\varphi_{\rm dS}\approx 157.1$. A tunable dS saddle or inflection point, which is responsible for inflation, is at $\varphi_{cr}\approx 144.5$.  There is a barrier at $\varphi \sim 200$ protecting the late-time dS minimum. The height of the barrier exceeds the height of the inflationary saddle/inflection point implying an absence of the cosmological overshoot problem~\cite{Brustein:1992nk,kaloper}.} \label{3}
\end{figure}

\begin{figure}
\centering{\includegraphics[height=6.5cm]{2dpot.eps}}
 \caption{The potential as a function of the complex field $T = \varphi +i\tau$,  in units of $10^{{-23}}$ of the Planck density. The inflationary saddle/inflection point and the late-time dS minimum both
occur at $\tau = {\rm Im}~T =0$, as shown in the analytic
investigation.} \label{4}
\end{figure}

One can then get a late-time de Sitter vacuum by adding, e.g. $\overline{\rm D3}$-branes, which due to warping provide for a hierarchically small supersymmetry breaking and uplifting term $C/\varphi^2$ in the scalar potential.\footnote{Alternatives include D-terms from a 4-cycle wrapping ${\rm D7}$-brane threaded by $F_2$-flux~\cite{Dterms}, F-terms of hidden sector matter fields~\cite{nilles} (see also~\cite{ReinoScrucca}), meta-stable vacua of condensing gauge theories in the free magnetic range along the lines of ISS~\cite{ISSmodels}, and $\alpha'$-corrections~\cite{alphaprimelift}} This lifting can then be used to either lift the smaller volume (and more shallow) AdS/Minkowski minimum eq.~\eqref{ReTcr} to a tiny positive value of the cosmological constant, or to lift the deeper AdS minimum eq.~\eqref{ReTAdS}. In this latter possibility,  the smaller volume minimum eq.~\eqref{ReTcr} becomes much more strongly lifted and acquires a large positive cosmological constant. Since in many cases it will still be separated from the lower dS minimum at larger volume by a barrier, this specific sub-setup realizes the situation depicted in the context of the toy model of the last Section in Fig.~\ref{Ramond}.

It is now clear that by tuning $W_0$ and (through their dependence on the VEV's of the complex structure moduli) also $A$ and $B$ with fluxes, we can arrange for the higher-lying minimum at smaller volume to degenerate with the barrier saddle point. As this will guarantee the existence of a very flat saddle or inflection point, which can lead to inflationary regime. For instance, a choice of parameters
\begin{eqnarray} W_0&=& 4\cdot 10^{-8},\ A=1,\ B=-0.62704017319,\nonumber \\ &&\\ a&=&\frac{2\pi}{58},\ b=\frac{2\pi}{60}\;{\rm and}\;C=3.01\cdot 10^{-18}\nonumber\label{input}\end{eqnarray}
for the full uplifted scalar potential
\begin{equation}
V= e^{K}\left(  G^{T \overline T} D_{T}W \overline {D_{T} W}
- 3|W|^2 \right)+\frac{C}{\varphi^2}
\end{equation}
leads - as discussed below - to a long period of volume modulus inflation of more than 190 e-folds.

The similarity of this model with the supergravity model of Ref. \cite{Holman:1984yj} is obvious when one compares Fig.~1 and  Fig.~\ref{3}, while Fig.~\ref{4} demonstrates that $\tau=0$ indeed denotes a local minimum in the axion direction for all values of $\varphi$.

We shall now describe the inflationary dynamics for the parameters chosen in eq.~\eqref{input} in more detail. For these parameters we find that the minimum given by eq.~\eqref{ReTcr} has already merged completely with the barrier saddle point to form a so-called inflection point: Instead of the former saddle point that provides for $\epsilon=0$ by definition and needs than $\eta$ to be tuned small, we now have a situation where $\eta=0$ at the inflection point and we have to keep $\epsilon$ small.

The slow-roll parameters of the inflection point have now to be given for the case of non-canonically normalized scalar field, as the metric on scalar field space for $\varphi$ is given by $g_{\varphi\varphi}=3/2\varphi^2$~\cite{Blanco-Pillado:2004ns}. Since the inflaton trajectory is one-dimensional (as we are in the local minimum of the axion direction, there is no field evolution in this direction), we arrive for the chosen set of parameters at values~\cite{Blanco-Pillado:2004ns}
\begin{eqnarray} \epsilon&=&\frac{g^{\varphi\varphi}}{2}\left(\frac{\partial_\varphi V}{V}\right)^2=\frac{\varphi^2}{3}\left(\frac{\partial_\varphi V}{V}\right)^2=1.8\cdot 10^{-18}\nonumber\\ && \\ \eta&=&g^{\varphi\varphi}\frac{\partial_\varphi^2 V}{V}=\frac{2\varphi^2}{3}\frac{\partial_\varphi^2 V}{V}\equiv 0\nonumber\end{eqnarray}
at the inflection point at $\varphi_{cr}=144.4588$.

\begin{figure}[ht!]
\centering\leavevmode\epsfysize=5.4cm \epsfbox{evolution.eps} \caption{The evolution of the volume modulus $t$ as a function of the total number of e-folds $N$.} \label{efolds}
\end{figure}

The corresponding inflationary regime can be directly seen by numerically solving the equations of motion for $\varphi$. In transforming into measuring time by e-folds $N$
\begin{equation} \frac{\partial \varphi}{\partial t}=H\frac{\partial \varphi}{\partial N}\equiv H\varphi' \end{equation}
with
\begin{eqnarray} H^2&=&\frac{1}{3}\left(\frac{1}{2}g_{\varphi\varphi} \dot\varphi^2+V(\varphi)\right)\nonumber\\ &=&\frac{1}{3}\frac{V(\varphi)}{1-\frac{1}{6}g_{\varphi\varphi} \varphi'^2}\end{eqnarray} we get the equation of motion to be~\cite{Blanco-Pillado:2004ns,noncanon}
\begin{eqnarray}
 \varphi''&=&-\left(1-\frac{1}{6}g_{\varphi\varphi} \varphi'^2\right)\left(3\varphi'+3g^{\varphi\varphi}\frac{V_{,\varphi}}{V}\right)\nonumber\\
 &-&\frac{\varphi'^2}{2}\frac{\partial\ln(g_{\varphi\varphi})}{\partial\varphi}\;.\label{eom}
\end{eqnarray}
Here we have allowed for a non-canonical kinetic term ${\cal L}_{\rm kin}=\frac{1}{2}g_{\varphi\varphi}\partial_\mu\varphi\partial^{\mu}\varphi$, as this is the generic case when dealing with moduli.

According to eq.~\eqref{eom} and plugging in $g_{\varphi\varphi}$, the equation of motion for the volume modulus $\varphi$ then takes the form~\cite{Blanco-Pillado:2004ns}
\begin{equation}
\varphi''=-\left(1-\frac{\varphi'^2}{4\varphi^2}\right)\left(3\varphi'+2\varphi^2\frac{V_{,\varphi}}{V}\right)+\frac{\varphi'^2}{\varphi}\;.\label{teom}
\end{equation}
Starting at the inflection point $\varphi(t =0)=\varphi_0$ with $\dot \varphi(0)=0$, this leads to about 193 e-folds of slow-roll inflation, before the volume modulus rolls off into the late-time dS minimum at $\varphi_{\rm dS}\approx 157.1$. The CMB scales of COBE normalization at about $k_{\rm CMB}\simeq 0.002/{\rm Mpc}$  leave the horizon about 60 e-folds before the end of inflation, i.e. here at $N_{\rm CMB}\approx 133$. The magnitude of the primordial curvature perturbation $\Delta_{\cal R}^2$ generated at this point evaluates for the parameters chosen to be
\begin{equation} \Delta_{\cal R}^2=\frac{1}{8\pi^2}\frac{H^4}{{\cal L}_{\rm kin}}=\frac{1}{4\pi^2}\frac{H^2}{g_{\varphi\varphi}\varphi'^2}\approx 2.9\cdot 10^{-9}\end{equation}
which agrees with the measured value of COBE and WMAP~\cite{WMAP}.
In Fig.~\ref{efolds} we see the last 20 e-folds of the $t$-evolution. Note the sharp end of inflation at $N_{\rm tot}\approx 193.5$ and the subsequent onset of oscillations.

Next, the spectral index of the curvature perturbation power spectrum is given by \begin{equation}
n_s=1+\left.\frac{d\ln \Delta_{\cal R}^2(k)}{d\ln
k}\,\right|_{k=RH}\label{specind2}\end{equation} evaluated as usual at horizon crossing.
Note that here we can replace $d\ln k\simeq dN$ because $k$ is evaluated at
horizon crossing $k=RH\sim H e^N$. Then we arrive at \begin{equation} n_s=1+\left.\frac{d\ln\Delta_{\cal R}^2(k)}{dN}\right|_{k=RH}\end{equation} which results in the curve shown in
Fig.~\ref{specindex}.

\begin{figure}[ht!]
\vspace*{0.5cm}
\centering\leavevmode\epsfysize=5.3cm \epsfbox{specindex.eps} \caption{The spectral index of the density fluctuations as a function of the total number of e-folds $N$. The blue arrow denotes the spectral index at the time when the COBE normalization scale left the horizon, i.e. at $N_e^{\rm CMB}=60$ e-folds before the end of inflation.} \label{specindex}
\end{figure}

This evaluates at the COBE normalization scale
\begin{equation} n_s\approx 0.93\end{equation}
Within the $1\sigma$-level this result agrees
with the combined 3-year WMAP + SDSS galaxy survey
result $n_s=0.948^{+0.015}_{-0.018}$~\cite{WMAP} (the 3-year WMAP
data alone give $n_s=0.951^{+0.015}_{-0.019}$).

We note further, that there is only negligible running at CMB scales as the third order slow-roll parameter evaluates to be $\xi^2\approx -7\cdot 10^{-4}$ which then gives $dn_s/d\ln k=2\xi^2\approx-0.0014$, and an extremely small level of tensor fluctuations as $\epsilon\approx 5 \cdot 10^{-17}$ at CMB scales.

\section{Basics of fine-tuning in generic models}\label{toyinf}

Now that we have two simple models of accidental inflation with an inflection point, the supergravity model of \cite{Holman:1984yj} and the string inflation model described in the previous section, and also the models of brane inflation  \cite{Baumann:2007np,delicate,Krause:2007jk,Panda:2007ie,Itzhaki:2007nk} and MSSM inflation  \cite{Allahverdi:2006we}, we can analyze general features of the models of this type.

Fine-tuning in the model \cite{Holman:1984yj} can be described in the following general way. If one takes $\Phi_{0}> 1$ in this model, one will have a potential with a metastable dS minimum at $\varphi < 0$ very close to the local maximum at $\varphi > 0$, see Fig. 1. If the difference $\Phi_{0}- 1$ is sufficiently small, then in the first approximation the term $V_{0}$ and the coefficient in front of $\varphi^{3}$ in (\ref{cubic}) will not change, but two other terms with very small coefficients $\lambda_{1},\lambda_{2} \ll 1$ will appear:
\begin{equation}\label{cubic2}
V(\varphi) =V_{0}\, \bigl(1 + \lambda_{1}\varphi + \frac{\lambda_{2}}{ 2} \varphi^{2}-\sqrt 2\, \varphi^{3} + O(1)\,\varphi^{4}\bigr) \ .
\end{equation}
In the limit $\Phi_{0} \to 1$, the metastable minimum moves towards the local maximum, and they form an inflection point. This corresponds to the limit $\lambda_{1},\lambda_{2} \to 0$.  The slow-roll parameters at $\varphi = 0$ are directly related to $\lambda_{1}$ and $\lambda_{2}$:
\begin{eqnarray}
\epsilon &=& \frac{1}{2}\left(\frac{V'}{V}\right)^{2} = \frac{1}{2} \lambda_{1}^{2} \ ,\nonumber\\
\eta &=& \frac{V''}{V} =    \lambda_{2} \ .
\end{eqnarray}

Thus in order to achieve inflation one should first find a potential with a metastable dS minimum close to a local maximum of $V(\varphi)$, and then change the parameters in such a way as to make these two extrema very close, which automatically will make the slow-roll parameters small. The required fine-tuning can be expressed in terms of the fine-tuning of the parameters $\lambda_{1}$ and $\lambda_{2}$.

One can look at this situation from a slightly different but closely related perspective. In accidental inflation, by definition, inflation occurs by chance, in a small vicinity of some point which can be called $\varphi =0$ without any loss of generality.
Consider the potential in a vicinity of this point and expand it in powers of $\varphi$:
\begin{equation}\label{cubic1}
V(\varphi) =V_{0}\, \Bigl(1 + \lambda_{1}\varphi + \frac{\lambda_{2}}{ 2} \varphi^{2} + \frac{\lambda_{3}}{3}\, \varphi^{3} + \frac{\lambda_{4}}{4}\,\varphi^{4}+...\Bigr)
\end{equation}
If the potential has flat directions, as in the simplest versions of chaotic or natural inflation, then one may consider theories where only few first terms are present \cite{Linde:2007fr}. However, in most of the versions of string inflation all  parameters $\lambda_{n}$ can be large, so making some of them small requires fine-tuning. Slow roll inflation is possible for $|\varphi | \ll 1$ if $|\lambda_{1}| \ll 1$ and $|\lambda_{2}|\ll 1$. We will assume that $\lambda_{3} \gtrsim 1$, which is indeed the case in the two models which we considered so far. Unless one fine-tunes $\lambda_{4} \gg \lambda_{3}$, one can ignore the quartic term while describing inflation at  $\varphi \ll 1$. This means that  in accidental inflation, which occurs only at $\varphi \ll 1$, it is generically sufficient to use only three first terms in the expansion of the potential.

Moreover, one can show that by a shift $\varphi \to \varphi + \Delta$ in a theory with $\lambda_{1},\lambda_{2} \ll 1$, $\lambda_{3} \gtrsim 1$, one can always represent the potential (\ref{cubic1}) in the form where either $\lambda_{1} = 0$, or $\lambda_{2} = 0$. For example, in the model of Ref. \cite{Holman:1984yj}  one has three possibilities illustrated by Fig. 1.
For $\Phi_{0} = 1$ one has an inflection point at $\varphi = 0$ where $\lambda_{1} = \lambda_{2} = 0$. For $\Phi_{0} > 1$ inflation begins near a local maximum of the potential at $\varphi > 0$. If one makes a change of variables $\varphi \to \varphi + \Delta$, where $\Delta$ corresponds to the position of this maximum, the potential acquires the form
\begin{equation}\label{23}
V(\varphi) =V_{0}\, \Bigl(1 +  \frac{\lambda_{2}}{ 2} \varphi^{2} + \frac{\lambda_{3}}{3}\, \varphi^{3} + ...\Bigr) \ .
\end{equation}
with $\lambda_{2} < 0$. Meanwhile for $\Phi_{0} > 1$ one can always make a change of variables bringing the potential to the form
\begin{equation}\label{13}
V(\varphi) =V_{0}\, \Bigl(1 +  {\lambda_{1} } \varphi  + \frac{\lambda_{3}}{3}\, \varphi^{3} + ...\Bigr) \ .
\end{equation}

We ignored here the quartic term because  accidental inflation,  by definition, occurs only for $|\varphi| \ll 1$. Therefore, unless one makes an additional fine-tuning $\lambda_{3} \ll \lambda_{4}$, one can ignore the term $\frac{\lambda_{4}}{4}\,\varphi^{4}$ in the description of inflationary dynamics in these models.\footnote{We should emphasize that some of our conclusions are based on the assumption that in the class of the models we study now inflation occurs only for $|\varphi| \ll 1$, which is the trademark of accidental inflation. In other words, we study generic features of the worst case scenario. It should remain our goal to search for the models with large flat directions.}

An important exception is represented by the models where the potentials have a maximum with $Z_{2}$ symmetry $\varphi \to -\varphi$. In this case
\begin{equation}\label{24}
V(\varphi) =V_{0}\, \Bigl(1 + \frac{\lambda_{2}}{ 2} \varphi^{2} + \frac{\lambda_{4}}{4}\,\varphi^{4}+...\Bigr)  \ ,
\end{equation}
and the required fine-tuning is $|\lambda_{2}|\ll 1$. In this case inflation is most efficient in the limit  $\lambda_{2} \to 0$, which corresponds to the purely quartic potential with $\lambda_{4} < 0$. This is what happens in the original versions of the new inflation scenario \cite{New}. This regime was also found in the racetrack inflation models \cite{Blanco-Pillado:2004ns}, where inflation occurs during the rolling in the axion direction from the saddle point of the potential.

Note that it is insufficient to simply take  $\lambda_{1}\ll 1$ or $\lambda_{2} \ll 1$, respectively, in our models. The required fine-tuning should be somewhat stronger as we want to achieve more than 50 or 60 e-folds of inflation.

As an example, one may consider the potential \eqref{13} describing an inflection point  and check how small should be the constant $\lambda_{1}$. Investigation of this situation was performed in~\cite{delicate}, and result for the total number of e-folding during inflation is
\begin{equation}
N_{\rm tot}=\int_{0}^\infty \frac{ V d\varphi}{V'} = \int_{0}^\infty \frac{d\varphi}{\sqrt{2\epsilon}}=\frac{\pi}{2}\frac{1}{\sqrt{\lambda_1\lambda_3}} \ .\label{NtotBaum}
\end{equation}
In order to avoid significant running of the spectrum, one must have $N_{\rm tot} \gg N_e^{\rm CMB}\simeq 60$. This leads to a condition
\begin{equation}
\lambda_{1} \ll 10^{{-3}} \lambda_{3}^{{-1}} \lesssim 10^{-3} \ ,\label{tunerunning}
\end{equation}
whereas we already assumed that $\lambda_{3} \gtrsim 1$ (this assumption is justified below). Thus we must have fine-tuning at least of the order $10^{-3}$.  We must fine-tune $\lambda_{2}$ in a similar way in the models (\ref{23}), (\ref{24}).

While this fine-tuning  is certainly not nice, in the next section we will explain  possible reasons which may make it looking quite natural.

The values of the slow roll parameters, the duration of inflation,  and the spectral index $n_{s} $  depend only on the $\lambda_{n}$, but they do not depend on the overall factor $V_{0}$. Meanwhile the square of the amplitude of metric perturbations $\Delta_{\cal R}^2$ scales as $V_{0}$. This allows to achieve an inflationary regime with desirable properties by fine-tuning  $\lambda_{1}$ or $\lambda_2$, and then   dial the desirable amplitude of perturbations of metric by changing $V_{0}$ without changing $\lambda_{n}$ any further \cite{Blanco-Pillado:2004ns}.

\section{Classical rolling versus quantum diffusion}\label{diffusion}

The structure of the model discussed before -- inflation starts driven by a single field direction from either a flat saddle or a flat inflection point of the potential -- lends itself to an analytical treatment of the inflationary dynamics with respect to the properties of the power spectrum of density fluctuations generated during slow-roll.

The starting point is the observation, that due to the fact that the whole inflationary dynamics is governed by very small field displacements $\Delta \varphi\ll 1$ away from the saddle/inflection point at $\varphi_{\rm cr}$, we can canonically normalize the field $\varphi$ in the vicinity of the unstable point and describe its motion by expanding the potential around the unstable point and `renormalizing' every derivative with respect to $\varphi$ as $\partial_\varphi \to \sqrt{g^{\varphi\varphi}(\varphi_{\rm cr})}\, \partial_\varphi$. This leads to slow-roll parameters defined as
\begin{eqnarray} \epsilon&=&\frac{\varphi_{\rm cr}^2}{3}\left(\frac{\partial_\varphi V}{V}\right)^2\nonumber\\ && \\ \eta&=&\frac{2\varphi_{\rm cr}^2}{3}\frac{\partial_\varphi^2 V}{V}\quad.\nonumber\end{eqnarray}
Next, we write the expansion eq.~\eqref{cubic1} of the potential around the unstable point as
\begin{equation}\label{Vexp}
V(\varphi) =  V_0\left(1+\sum_{p\geq 1}\frac{\lambda_p}{p}\,\varphi^p\right) \ .
 \end{equation}
Here $\lambda_p=(g^{\varphi\varphi})^{p/2}\, {V^{(p)}_0}/{V_0}$, \,
$V_0^{(p)}=\partial_\varphi^p V(\varphi_{\rm cr})$, {and we replace }\, $\varphi\to \varphi+\varphi_{\rm cr}$,
 so that $\varphi=0$ now denotes the critical point and $\varphi$ denotes what was $\Delta\varphi$ before.

Depending on whether the potential is monotonic around the unstable point or not, we get either an expansion around an inflection point solving $\lambda_2\sim\partial_\varphi^2 V(\varphi_{\rm cr})=0$ or a saddle point solving $\lambda_1\sim\partial_\varphi V(\varphi_{\rm cr})=0$. Successful inflation requires us then to tune small either $\lambda_1$ (inflection point) or $\lambda_2$ (saddle point).

Following the discussion of the last Section, we can thus parametrize the leading approximation to the potential in the two cases as
\begin{equation}
V=\begin{cases}V_0\left(1-\lambda_1\varphi-\frac{\lambda_3}{3}\varphi^3\right)  & \text{for an inflection point}\\
V_0\big(1+\frac{\lambda_2}{2}\varphi^2\pm\frac{\lambda_p}{p}\varphi^p\big) & \text{for a saddle}
\end{cases}\end{equation}
where we have
\begin{equation}
\lambda_2=\eta_0\equiv\eta(0)=-m^2/V_0<0\ .
\end{equation}

We subdivide the second case into saddle points which are subject to a symmetry $Z_2:\,\varphi\to-\varphi$ (then $p=4+2n,~n\in \mathbb{N}$ starts with 4) and saddle points which are not (then p starts with 3).

We can then compute within the validity of the slow-roll regime the number of e-foldings $N_e(\varphi)$ counting backwards from the value $N_e(\varphi_{\rm end})\equiv 0$ at the end of inflation at $\varphi_{\rm end}$
\begin{equation}
N_e(\varphi)=\int_{\varphi_{\rm end}}^\varphi \frac{d\varphi}{\sqrt{2\epsilon}}\;.
\end{equation}
This integral can be performed in closed form in both cases. From the expression for $N_e(\varphi)$ we can then express the slow-roll parameters $\epsilon$ and $\eta$ as function of $N_e$.

Since we need to fine-tune $\lambda_{1}, \lambda_{2}$ to be extremely small, we will start our investigation with the study of the simple model
\begin{equation}
V=V_0\left(1-\frac{\lambda_p}{p}\varphi^p\right) .\label{Vsimp}
\end{equation}
In this simplified situation we have
\begin{equation}
N_e(\varphi_N)=\frac{1}{p-2}\cdot\frac{1}{\lambda_p\varphi_N^{p-2}}\ , \label{NePbic}
\end{equation}
where we have taken $\varphi_{\rm end}\to\infty$ as this does not change the result significantly. From this expression we find the slow-roll parameters to be
\begin{eqnarray}\label{etansPbic}
\epsilon&=&\frac{1}{2(p-2)^{2\frac{p-1}{p-2}}}\lambda_p^{-\frac{2}{p-2}} N_e^{-2\frac{p-1}{p-2}}\nonumber\\ && \\ \eta&=&-\,\frac{p-1}{p-2}\cdot\frac{1}{N_e}\quad.\nonumber
\end{eqnarray}
We can then compute the density fluctuations at $N_e$ e-folds before the end of inflation
\begin{eqnarray}\label{DensflucAnalyt}
\left.\Delta_{\cal R}^2\right|_{N_e}&=&\frac{1}{4\pi^2}\left(\frac{H^2}{\dot\varphi}\right)_{N_e}^2=\frac{1}{24\pi^2}\left.\frac{V}{\epsilon}\right|_{N_e}\ , \nonumber\\ &&
 \\
&=&\frac{V_0(p-2)^{2\frac{p-1}{p-2}}}{12\pi^2}\lambda_p^{\frac{2}{p-2}} N_e^{2\frac{p-1}{p-2}}\ .\nonumber\end{eqnarray}

As the quantity $\left.\Delta_{\cal R}^2\right|_{N_e}$ is constrained by the COBE and WMAP results at the scale of $N_e=N_e^{\rm CMB} \sim 60$, this equation leads to a relation between the scale of the potential $V_0$ and its small-field power-law behavior controlled by $\lambda_p$.

We shall illustrate this constraint for the case $p=3$ of the explicit string model of the Section~\ref{KLinf} where
\begin{equation}
p=3\ ,\quad \lambda_3\approx 3.7\cdot 10^{4}\ ,\quad V_0\approx 2.7\cdot 10^{-23} \ , \label{ExampleVal}
\end{equation}
which implies then from the eq.~\eqref{DensflucAnalyt} above that
\begin{equation}
{V_0} \approx  3\cdot 10^{-14}\, \lambda_3^{-2}
\end{equation}
in units of Planck density. (In our paper we use Planck mass $M_{\rm P}=2.4\cdot 10^{18}\,{\rm GeV}$ and work in units $M_{p}= 1$.)

Upon inspection of eq.~\eqref{NePbic} we might conclude that the total number of e-folds is infinite if we were to start inflation at $\varphi\to0$. However, our classical equations ignored quantum diffusion of the field $\varphi$, which is important near the point $\varphi = 0$.

Indeed, the field does not move classically from this point because $V' = 0$ there. However, the long-wavelength perturbations grow as follows:
\begin{equation}
\langle \varphi^{2} \rangle  = \frac{H^{3}}{4\pi^{2}}t \ .
\end{equation}
  These perturbations are stretched by inflation, and therefore for all practical purposes they look as a nearly homogeneous classical field with a typical magnitude
\begin{equation}
\varphi = \sqrt{\langle \varphi^{2} \rangle}  = \frac{H}{2\pi }\sqrt {Ht} \
\end{equation}
and speed
\begin{equation}
\dot \varphi   = \frac{H}{4\pi }\sqrt \frac{H}{ t} = \frac{H^{3}}{8\pi^{2} \varphi} \  .
\end{equation}
The speed of the classical motion,  $\dot\varphi = V'/3H$,  becomes greater than the speed of diffusion for
\begin{equation}
|\varphi\, V'| = V_{0 }\lambda_{p} \varphi^{p} > \frac{V_{0}^{2}}{24\pi^{2}} \ .
\end{equation}
Thus  the field grows due to quantum diffusion until some moment $\bar t$ when its average value grows up to
\begin{equation}\label{phibar}
\bar\varphi  \sim \left(\frac{V_{0}}{24\pi^{2}\lambda_{p}}\right)^{1/p} \ .
\end{equation}
During this part of the process the size of the universe grows by a factor of $e^{\bar N} \sim e^{H\bar t}$, where
\begin{equation}
\bar N \sim \lambda_{p}^{-2/p}\, V_{0}^{2/p - 1}\frac{(24\pi^{2})^{1-2/p}}{2} \ .
\end{equation}
After that, the universe continues growing in the classical regime. According to Eq. (\ref{NePbic}), the number of e-folds in this regime is given by
\begin{equation}\label{expen}
N_e(\bar\varphi)\sim \lambda_{p}^{-2/p}\, V_{0}^{2/p - 1}\frac{(24\pi^{2})^{1-2/p}}{p-2}=\frac{2\bar N}{p-2} \ .
\end{equation}
This gives
\begin{equation}\label{expen2}
N_{\rm tot} = \bar N + N_{e}\sim \frac{1}{2}\lambda_{p}^{-2/p}\, V_{0}^{2/p - 1} (24\pi^{2})^{1-2/p}\ \frac{p}{p-2} \ .
\end{equation}

Let us consider now a realistic situation with $p = 3$, $\lambda_{3} = 1$ and $V_{0} \sim 3\times 10^{{-14}}$. In this case the total growth of volume of the universe can be estimated by
\begin{equation}
e^{3N_{\rm tot}} \sim e^{10^{6}} \ .
\end{equation}
The analogous result for the quartic potential, p = 4, with $\lambda_{4} = O(1)$, is
\begin{equation}
e^{3N_{\rm tot}} \sim e^{3\cdot 10^{8}} \ .
\end{equation}

Notice that the expression for $N_{\rm tot}$ still diverges for $\lambda_p\to0$. Clearly, this divergence is unphysical as for $\lambda_p\lesssim 1$ we would find that the potential reaches $V \approx 0$ only for $\varphi >1$ in Planck units. This would lead to chaotic inflation at large $\varphi$, which should be treated separately.

In this paper we consider  only situations where $\varphi\ll 1$, $\lambda_p\gtrsim 1$. In the explicit realization of the Section~\ref{KLinf} this always fulfilled by a large margin, $\lambda_p\gg 1$, once one expands the potential there around $t_{\rm cr}$ according to eq.~\eqref{Vexp}. Furthermore, demanding $\lambda_p\gtrsim 1$ implies that $\bar\varphi\sim V_0^{1/p}\ll 1$ as long as $V_0\ll 1$ which justifies the simplifications made before in that the inflationary process really takes place very close to the unstable point.

The constraint $\lambda_p\gtrsim 1$ plugged into eq.~\eqref{etansPbic} implies an upper bound on $\epsilon$ as now we have
\begin{equation}
\epsilon \lesssim N_e^{-2\frac{p-1}{p-2}}\leq \frac{1}{N_e^4}\quad\text{for }p\geq 3\quad.
\end{equation}
Further, from eq.~\eqref{etansPbic} we have a spectral index~\cite{LythRiotto,hilltop}
\begin{equation}
n_s=1+2\eta=1-2\,\frac{p-1}{p-2}\cdot\frac{1}{N_{e}} \ .\label{nsAnalyt}
\end{equation}

Observationally we probe $N_e=N_e^{\rm CMB}\simeq 60$. Thus, we infer an immeasurably low fraction $r=12.4\,\epsilon_{60}\lesssim 10^{-6}$ of power in gravitational waves and a spectral index which changes from $0.93$ for $p = 3$ to $0.97$ for $p \gg 3$.

We may now test our methods by applying them to the explicit string theory model proposed in Section \ref{KLinf}. Instead of calculating the amplitude of perturbations directly, we may represent the potential as a sum of terms $\lambda_{n}\varphi^{n}$ up to $n = 3$ using eq.~(\ref{Vexp}), and then use the methods developed in this section. Using the values of eq.~\eqref{ExampleVal} gives us in terms of eq.s.~\eqref{DensflucAnalyt} and \eqref{nsAnalyt}
\begin{equation}
\Delta_{\cal R}^2\approx 4\cdot 10^{-9}\ ,
\quad n_s\approx 0.93\ ,
\end{equation}
which are evaluated at the time of horizon crossing of the CMB normalization scale modes at $N_e\simeq 60$.
The agreement with the numerical results of  Section \ref{KLinf} is good enough to justify the use of the simplified potential, where we have neglected the small linear term and higher powers $p\geq 4$.

For completeness, we note that the analogous treatment of the important exception represented by a $Z_2$-symmetric saddle point (quartic potential with a very small quadratic piece) yields
\begin{equation}
n_s^{(p=4)}=1-\frac{3}{N_e^{\rm CMB}}\approx 0.95\ .
\end{equation}

Finally, we may give here the results for $N_{\rm tot}$ and $n_s$ for finite values of $\lambda_{1,2}$.

We will consider the case of a $p=3$ inflection point with finite $\lambda_1$ and a general $p\geq 3$ saddle point with finite $\lambda_2$. In this situation, $N_{\rm tot}$ and $n_s$ will be a function of $\lambda_1$ or $\lambda_2$, respectively, for fixed $\lambda_p,\; p\geq 3$. We get again
\begin{equation}
N_{\rm tot}\simeq N_e(\bar\varphi)\simeq \frac{\pi}{2}\frac{1}{\sqrt{\lambda_1\lambda_3}}\quad\text{if: }\lambda_1\gtrsim\lambda_3\bar\varphi^2 \sim 10^{-10}
\end{equation}
for the $p=3$ inflection point and
\begin{equation}\label{Ntotsaddlepoint}
N_{\rm tot}\simeq N_e(\bar\varphi)=\frac{\lambda_2^{-1}}{p-2}\ln(1-\lambda_2\lambda_p^{-1}\bar\varphi^{2-p})
\end{equation}
for the saddle point. Using these expressions we can compute $\eta(N_{\rm tot})$ by expressing $\lambda_{1,2}$ through the appropriate $N_{\rm tot}$ and we get $n_s(N_{\rm tot})$. The results are~\cite{delicate,Aterm}
\begin{eqnarray}
n_s&=&1+2\eta=1-\frac{2\pi}{N_{\rm tot}}\cot\left(\frac{\pi N_e}{2N_{\rm tot}}\right)\nonumber\\ &=&1-\frac{4}{N_e}\ ,\quad\text{for }N_{\rm tot}\gg N_e\label{nsinflec}
\end{eqnarray}
for the $p=3$ inflection point and
\begin{eqnarray}\label{nssaddle}
n_s&=&1+2\eta=1-2\lambda_2\left(1+\frac{p-1}{e^{(p-2)\lambda_2 N_e}-1}\right)\nonumber\\ &=&1-2\frac{p-1}{p-2}\cdot\frac{1}{N_e }\ ,\\&&\nonumber \\
&&\quad\text{for}\; \ N_{\rm tot}\gg N_e\quad\Leftrightarrow\quad  |\lambda_2|=|\eta_0|\ll 1\;.\nonumber
\end{eqnarray}
for a saddle point~\cite{Aterm}, where $\lambda_2=\lambda_2(N_{\rm tot})$ is the inverse of eq.~\eqref{Ntotsaddlepoint}.

We see that  we get back the results valid in the pure $\lambda_p\varphi^p$-potential for $N_{\rm tot}\gg N_e$ which corresponds to either very small $\lambda_1$ or $\lambda_2$. This behavior is displayed in Fig.~\ref{specindex_analytic} for the three cases of a $p=3$ inflection point (solid black), a $p=3$ saddle point (dash-dot black), and a $p=4$ $Z_2$-symmetric saddle point (solid red).

\begin{figure}[ht!]
\hspace*{-0.2cm}\leavevmode\epsfysize=5.6cm \epsfbox{specindex_analytic.eps} \caption{The spectral index $n_s$ as a function of the total number of e-folds $N_{\rm tot}$ at the COBE scale, i.e. in eq.s~\eqref{nsinflec} and \eqref{nssaddle} at $N_e=N_e^{\rm CMB}=60$. Black: The solid line corresponds to the $p=3$ inflection point. The dash-dotted line represents the $p=3$ saddle point case. The dashed horizontal line is their common asymptotic value $n_s=0.933$. Red: The solid line gives $n_s(N_{\rm tot})$ for the case $p=4$ with a $Z_2$-symmetry, as e.g. realized in the model of `racetrack inflation'~\cite{Blanco-Pillado:2004ns}. From there the values of $V_0$ and $\lambda_4$ have been extracted using eq.~\eqref{Vexp} analogously to the $p=3$ case treated here explicitly. This allows to compute $n_s(N_{\rm tot})$ in the same way. The dashed horizontal line gives the $p=4$ asymptotic value of $n_s=0.95$.} \label{specindex_analytic}
\end{figure}

\section{Spectral index $n_{s}$ for accidental inflation}\label{predict}

\subsection{Naturalness of fine tuning}

We can now re-enter the linear or quadratic term, respectively, into the two cases of an inflection or a saddle point. Keeping them will enable to derive the dependence of spectral properties like $n_s$  on $\lambda_{1}$ and $\lambda_{2}$.

Let us see first what will happen if we add back to our cubic potential the term $\lambda_{1}\varphi$ with $\lambda_{1} < 0$. In this case the field $\varphi$ will roll down a bit faster, and the total number of e-folding will be smaller. The corresponding effect will be relatively insignificant if
\begin{equation}\label{tuning}
|\lambda_{1}| \ll  |\lambda_{3}|\bar\varphi^{2} \sim (24\pi^{2})^{-2/3} \, |\lambda_{3}|^{1/3} V_{0}^{2/3}  \ .
\end{equation}
For example, if one considers the semi-realistic case
$\lambda_{3} = {\cal O}(1)$ and $V_{0} \sim 3\cdot 10^{{-14}}$, this constraint means that for
\begin{equation}\label{tuning2}
|\lambda_{1}| \ll  10^{{-10}}
\end{equation}
the average total growth of volume during inflation in  a vicinity of any given point will remain as large as $e^{3 \cdot 10^{5}}$. On the other hand, if we consider the case which, naively, would seem much more natural, $|\lambda_{1}|\gg 10^{-10}$, then the average total growth of volume during inflation will become exponentially smaller. As we already mentioned, the total degree of inflationary expansion will exceed the required 60 e-foldings for much smaller fine-tuning, $|\lambda_{1}| < 10^{{-3}}$, but it produces a growth of volume which is smaller than the volume produced for $|\lambda_{1}| \ll 10^{-10}$ by the enormous factor of $e^{-3 \cdot 10^{5}}$.

Now let us discuss the fine tuning of initial conditions in accidental inflation. According to (\ref{phibar}), if initially the absolute value of the field $\varphi$ in our part of the universe was smaller than  $\bar\varphi  \sim \left(\frac{V_{0}}{24\pi^{2}\lambda_{3}}\right)^{1/3} \sim 10^{-5}$, then the volume of this part grows  by an enormous factor $e^{10^{6}}$ (for $\lambda_{3} \sim 1,  V_{0} \sim 3\times 10^{{-14}}$ and $\lambda_{1} \sim 10^{{-10}}$). However, if the field initially was at a greater distance from the inflection point, the gain in volume immediately becomes much smaller. This is an important fact to keep in mind while discussing naturalness of initial conditions for inflation. An additional factor is the process of eternal inflation, which also occurs only for small $\varphi$, see Appendix.

An interesting feature of our results is that the total growth of volume does not increase when we fine-tune $\lambda_{1}$ with an accuracy greater than $10^{-10}$. In other words, our considerations do not predict $\lambda_{1} = 0$; they predict $\lambda_{1} \sim 10^{{-10}}$.

Similarly, if we add the quadratic term $\lambda_{2} \varphi^{2}/2$ to the model with $\lambda_{3} = O(1)$ and $V_{0} \sim 10^{{-14}}$, the total amount of inflation will be unaffected for $|\lambda_{2}| \ll  10^{{-5}}$,
and it will decrease dramatically for $|\lambda_{2}| \gg  10^{{-5}}$.

Finally if we consider the $Z_2$-symmetric class of models with a quartic potential with $\lambda_{4} = O(1)$, and add to it the quadratic term $\lambda_{2} \varphi^{2}/2$, then the average total growth of volume during inflation in  a vicinity of any given point remains in the range of $e^{8 \cdot 10^{7}}$ for $|\lambda_{2}| \ll  10^{{-10}}$, and it will rapidly drop down for $|\lambda_{2}| \gg  10^{{-10}}$.

Let us now discuss the consequences of these results for understanding of naturalness/unnaturalness of fine-tuning required for accidental inflation. Here we should remember that inflation in string theory landscape is always eternal because of the existence of an incredibly large number of metastable vacua \cite{Lerche,Bousso,KKLT,Susskind:2003kw, Douglas:2003um}. The problem of assigning probabilities for various histories in the eternal inflation scenario is still a subject of intense debates. One of the popular ideas is that the probability to be born in a particular part of the landscape is proportional to  the volume of the parts of the landscape of a given type, see e.g. \cite{LLM,Mediocr,Bellido2,Meas1,Linde:2006nw,LindeMeas,Hawking:2007vf} and references therein. Many authors agree that the volume-weighted probability should be proportional to the growth of volume during the slow-roll inflation \cite{Meas1,LindeMeas,Hawking:2007vf,LindeWinitz}.

If this is the case, then the results obtained above suggest that the fine-tuning of $\lambda_{1}$ and $\lambda_{2}$ required for accidental inflation is in fact quite natural; see \cite{Mediocr,Bellido2,Linde:2007fr} for a discussion of related ideas, and the Appendix of our paper where we reach similar conclusions using slightly different assumptions.

\subsection{A prediction for $n_s$}

These arguments also imply that the most probable values for the spectral index in this class of models will be the asymptotic values of eq.~\eqref{nsAnalyt} for the pure cubic (or quartic, in case of a $Z_2$-symmetric potential) case discussed above:

Using the volume-weighted measure, we should expect to find ourselves in a Hubble volume with a long period of slow-roll inflation in the past. And as we noted above, maximizing the amount slow-roll inflation implies having either $\lambda_1\to 0$ or $\lambda_2\to 0$ corresponding to a very large $N_{\rm tot}\gg N_e^{\rm CMB}$.

Looking again at Fig.~\ref{specindex_analytic}, it becomes clear that the asymptotic values of eq.~\eqref{nsAnalyt} for the pure cubic (or quartic, in case of a $Z_2$-symmetric potential)
\begin{equation}
\begin{cases} n_s\approx 0.93\quad\text{no }Z_2\text{-symmetry of }V\\
n_s\approx 0.95\quad Z_2\text{-symmetry of }V\quad
\end{cases}
\end{equation}
become a tentative prediction for accidental inflation in the string theory landscape. Together with the negligible tensor fraction $r<10^{-6}$ this is the hallmark of accidental inflation in string theory. We call this prediction tentative because it is based on certain assumptions about the probability measure. Moreover, it may change if we are allowed to fine-tune even further, by fine-tuning $\lambda_{3}$ to zero (which would lead to a greater value of $n_{s}$), changing $V_{0}$, the amplitude of density perturbations, etc., see the Appendix for a discussion of this issue.

\section{Conclusion}\label{concl}

We have shown that the generic presence of racetrack superpotentials together with fluxes leads to a realization of volume modulus inflation in type IIB string theory. The central observation there is that the multi-exponential superpotential generically leads to more than one local minimum. This can be used to tune the higher-lying of two adjacent minima to (nearly) degenerate with the separating barrier into a very flat saddle or inflection point, which then drives slow-roll inflation. Following these considerations, in Section \ref{KLinf} we constructed a model of volume modulus inflation, which is one of the simplest models of string theory inflation available now.

Inflation in a vicinity of an inflection or saddle point requires fine-tuning of the model parameters and of the initial conditions.
However, this simple setup describes both the majority of known closed-string modular inflation models~\cite{Blanco-Pillado:2004ns,alphaprime}, as well as the recently improved KKLMMT model~\cite{Baumann:2007np,delicate,Krause:2007jk,Panda:2007ie,Itzhaki:2007nk}.\footnote{The ${\rm D3}$-${\rm D7}$-brane inflationary scenario~\cite{D3D7} does not fall into this class as it leads quite naturally to hybrid inflation.} Thus, the dynamics of accidental inflation described in this paper may represent one of the most generic classes of inflationary models, covering a large part of the landscape. The required fine tuning may appear quite natural if one takes into account that it dramatically increases the total growth of volume during inflation, and may even make inflation eternal.

This fact  leads to a statistical prediction of the spectral index $n_s\approx 0.93$, or $n_s\approx 0.95$, depending on whether the potential is $Z_2$-symmetric or not. Furthermore, the value $n_s\approx 0.95$ for $Z_2$-symmetric potentials by means of this symmetry is an upper limit (see Fig.~\ref{specindex_analytic}) as long as we tune just the first even power in such a potential, i.e. $\lambda_2$. to zero (see also~\cite{Blanco-Pillado:2004ns,racetrns}). These results,  combined with a prediction of a negligibly small tensor to scalar ratio  $r<10^{-6}$,   become a testable (tentative) prediction for a large class of models of inflation in string theory.
\vskip 0.3cm

\noindent {\bf Acknowledgments}: It is a pleasure to thank R. Bousso, J. Conlon, R. Kallosh, F. Quevedo, V. Vanchurin, A.~Vilenkin and  S.~Winitzki for useful discussions. This work was supported in part by NSF grant PHY-0244728 and by the Alexander-von-Humboldt Foundation.

redpajama_set_name: RedPajamaArXiv


Fans of The Real Housewives of New Jersey know that Joe Gorga makes his money by flipping houses. This is the practice of buying houses, renovating them and selling them for a higher price.
Over the years on RHONJ, Melissa Gorga has attempted a singing career, opened a moderately successful clothing boutique and recently opened a restaurant with sister-in-law Teresa Giudice. Taking a page from her sister-in-law, Melissa also wrote a book. Instead of writing a cookbook like Teresa, Melissa wrote a book about the recipe for a hot and happy marriage.
Long-time viewers of the hit Bravo reality show know that Joe and Melissa Gorga fight a lot about one thing. This is the fact that she works outside of the home. Joe is a traditional Italian husband who expects his wife to be at home doing housework, cooking meals and waiting on him hand and foot.
Despite Joe's 1950s mindset on marriage, he is surprisingly supportive of Melissa's goals and dreams. He even built the boutique retail space for her, as well as their home.
Maybe the reason Melissa works so hard at her dreams is to match her husband's hard-working attitude. When he's not flipping houses, Joe holds seminars to teach others the house-flipping business. Tickets to the seminar are a measly $10,000 per ticket.
Melissa and Joe are hoping to land a spin-off, either on Bravo or another network, similar to the home improvement shows that are immensely popular on HGTV.
The couple recently put the house that Joe built on the market for $3.3 million. Since Melissa is in L.A. frequently for business, she joked that she plans to move there and join Real Housewives of Beverly Hills, another of Bravo's Real Housewives franchise set in the upscale 90210 zip code.
It remains to be seen if Joe and Melissa do pack up and move to L.A. or build another house in New Jersey. Given that Bravo has recently jumped into the home improvement TV niche, it's not entirely out the realm of possibility that Joe and Melissa will get their own show.
Or maybe Teresa and Joe Giudice will get their own show about Joe's upcoming deportation. Your move, Bravo.
Tune into The Real Housewives of New Jersey on Bravo for the all the table and house flipping fun!


text:
Swipe right for testing: gay dating app helps fight rising HIV in Bulgaria
by Sonia Elks | @SoniaElks | Thomson Reuters Foundation
Friday, 7 June 2019 09:48 GMT
Two HIV-positive men pose for a photograph at the office of Single Step LGBT+ organisation in Sofia, Bulgaria on May 31, 2019. Thomson Reuters Foundation / Getty Images for Gilead Sciences
Grindr users in Bulgaria are being offered free HIV self-testing kits to combat rising infection rates
By Sonia Elks
SOFIA, Bulgaria, June 7 (Thomson Reuters Foundation) - When an LGBT+ charity wanted to do something about soaring rates of HIV among gay men in socially conservative Bulgaria, they turned to an unlikely ally - the dating app Grindr.
Seeking to target sexually active gay men who might not otherwise get checked, the charity offered free HIV self-testing kits to all Grindr's users in the eastern European country.
"People don't get tested because of stigma," said Ivan Dimov of Single Step, the LGBT+ youth charity behind the project.
"Testing is associated with sexuality ... Going to a testing facility outside of Sofia in a way equates to revealing to that small community that you live in that you are gay."
HIV infections are falling across the world, but eastern Europe is bucking the trend - there, the annual number of new HIV infections has roughly doubled over 20 years.
In Bulgaria, the number of gay and bisexual men being infected is rising by nearly a third year-on-year, showed data from the health ministry presented at a conference last week.
"If this continues, it will turn into an epidemic," said Professor Hristo Taskov from the National Centre for Infectious and Parasitic Diseases.
TESTING DILEMMA
Testing is a key part of combating HIV and AIDS: people who do not know they are positive will not get access to treatment to preserve their own health and may also put partners at risk.
People who are unaware they have HIV are more likely to have unprotected sex, risking the spread of infection further, found a 2014 study in Mozambique.
Although HIV tests are anonymous, patients in Bulgaria were often required to identify themselves when they entered a health centre and reveal where they were going, said Momchil Baev, the sexual health programme manager at Single Step.
HIV testing vans used in rural areas were also highly visible and associated with stigma, he said.
The consequences of being outed could be devastating, especially outside the biggest cities, said gay men and LGBT+ health experts.
"I came out at age 17 and my mother took me to a psychiatrist to try to 'mend' me," said one gay man living in Sofia, who asked not to be identified.
"Society is homophobic in general and HIV is a complete taboo," he told the Thomson Reuters Foundation.
Coming out in rural areas is "absolutely impossible" , said Elena Birindzhieva from the LGBT+ health centre CheckPoint Sofia.
"There can be physical violence, there can be verbal aggression," she said.
Self-testing kits, which look and function much like home pregnancy tests, solve that problem by allowing complete anonymity.
Users must swipe saliva from their gums using a wand. After 20 minutes a window on the wand's handle will display one line if the test is negative and two lines if it is positive.
Grindr users were asked to fill in a survey giving basic details and were then able to order a test sent by post.
The test came with advice on HIV transmission risk, and Single Step ran a 24-hour hotline during the project to offer advice and support to those who tested positive.
Ivan Dimov, the founder of Single Step LGBT+ organisation, poses for a photograph at its office in Sofia, Bulgaria on May 31, 2019. Thomson Reuters Foundation / Getty Images for Gilead Sciences
'PRAGMATIC' SOLUTION
More than half the 1,500 people who filled out the initial survey said they did not know their HIV status and about one in four said they never or rarely used a condom.
Almost one in three said they had never been tested for HIV before, and a further quarter had not checked their status in more than a year.
A total of 900 people ordered tests and 332 people reported their results back to Single Step, of whom ten tested positive and were diagnosed with HIV.
"I am very proud of this campaign because we really designed it to address a problem," said Dimov.
"Together we designed something very pragmatic."
The project was among a handful experimenting with HIV self-testing aimed at LGBT+ people.
A similar scheme to distribute tests via popular gay dating websites is currently taking place in the Czech Republic.
A study looking at another pilot targeting Grindr users in the U.S. city of Los Angeles in 2014 concluded such schemes had "high potential to reach untested high-risk populations".
FUTURE MODEL?
Some critics have pointed out that asking users to test at home leaves them without expert support if they are positive.
There are also data risks for schemes run through social media - Grindr was thrust into a scandal last year when it emerged it had been sharing users' HIV status data with third-party app performance companies.
Grindr has stressed the data was only used to test new features and was never sold or available to advertisers.
Taskov also raised concerns over cost, saying the self-tests were considerably more expensive than a standard blood test.
However, advocates say that prevention is cheaper than treatment and HIV home tests have been commended by the World Health Organization, which says they have potential to reach groups who might not otherwise check their status.
"We wholeheartedly support widespread access to self-testing, ideally with free distribution campaigns focusing on populations most affected by HIV," said Daniel Simoes of the HIV testing initiative EuroTEST.
Single Step hoped their work could act as a model for other nearby countries facing similar issues over stigma, and they are already in talks with an LGBT+ group in Romania aimed at helping them to launch a similar scheme.
"It's not just this one little pilot project - I really think it can have wider impact," said Dimov.
(Reporting by Sonia Elks @soniaelks; Editing by Claire Cozens. Please credit the Thomson Reuters Foundation, the charitable arm of Thomson Reuters, that covers humanitarian news, women's and LGBT+ rights, human trafficking, property rights, and climate change. Visit http://news.trust.org)
LGBT - Health
Riskier male sex pushes Europe's syphilis rates up 70% since 2010
Suicide risk at crisis proportions among LGBT+ youth - U.S. research
U.S. psychoanalysts apologize for labeling homosexuality an illness
In first for Gabon, Dorothee finally feels like a woman after surgery

redpajama_set_name: RedPajamaCommonCrawl


PASMI Polish Association of Self Medication Industry, as a contents partner, takes part in the second edition of the campaign of the Supreme Pharmaceutical Chamber [NIA] and the National Drug Institute [NIL] titled "Uwaga na leki – grypa i przeziębienie" [Be careful of drugs – flu and cold], devoted to flue and cold.
The indicated initiative is aimed at increasing the awareness of Poles and changing inappropriate behaviors and habits related to the use of medicinal products and treatment of viral infections.
"PASMI's participation in the NIA and NIL educational project fits perfectly into one of the main statutory goals of the organization, which is educating patients in order to raise their awareness in the area of responsible and safe treatment. PASMI's invitation to substantive support of the campaign gives us the opportunity to share the knowledge on how to treat responsibly with the Polish patient." – says PASMI's President, Ewa Jankowska.
The task of the educational campaign "Be careful of drugs – flu and cold" is to provide patients with the most important information on what should be done on the first symptoms of the disease, why it is so important to distinguish a flu from a cold, and what to pay attention to during self-treatment. On www.uwaganaleki.pl website dedicated to the action, patients will also find important tips on when it is necessary to consult a doctor, and when you only need to stay at home and fight the symptoms, when the risk of complications increases, which drugs should not be combined and which ones are not recommended for children and pregnant and lactating women.


It was a bad night for reality TV veterans after Geordie Shore star Ricci Guarnaccio and TOWIE's Lauren Goodger were voted off Celebrity Big Brother.
The pair fell at the penultimate hurdle in Thursday's double eviction, leaving six housemates to battle it out for victory in Friday's grand finale.
And there were awkward moments between them on the couch with host Emma Willis when they discussed their on-off 'show-mance' after leaving the Celebrity Big Brother house.
Their departure leaves boxer Audley Harrison, Benefits Street star 'White' Dee Kelly, former B*Witched singer Edele Lynch, Hollywood actor Gary Busey, Gogglebox star George Gilbey and Strictly Come Dancing's James Jordan in with a chance of winning.
He said the pair 'clicked', but that while there was lots of flirting between them on some nights, during the day she would distance herself from him.
Lauren was booed by the crowd when she said Ricci was a 'wicked guy' and that she would always be friends with him, but said she felt under pressure and 'very cornered', and that he would only talk with her after he had a drink.
Ricci also defended fellow housemate James, saying he was simply 'mischievous' and that people had got him wrong.
And he described 70-year-old actor Gary, who has rubbed many of the housemates up the wrong way and left Edele in tears after being rude to her, as 'unbelievable' when speaking with him one-on-one, but very different in group situations.
Ricci also suggested there had been a few 'games' going on with it getting so close to the final, singling out boxer Audley for doing things to get noticed.
Lauren disagreed, saying Audley was 'very caring, very honest, very calm'.
Despite being voted off, Ricci said he would not change a thing about his experience in the house, despite 'every day' being hard.
Ricci and Lauren's departure follows that of boxing promoter Kellie Maloney, who was formerly known as Frank before undergoing hormone therapy shortly before the show started, and American reality TV star Stephanie Pratt, who were voted out in another double eviction last Friday.
They joined former Gladiator David McIntosh, US actor Leslie Jordan and reality television personality Angelique "Frenchy" Morgan in leaving the Channel 5 show.


text:
Powerful Changemaker, or Powerful Distraction?
By Manuel Mattke
Within the past few years, US schools are investing more money into educational technology. For example, in 2015, K-12 schools spent close to $6 billion on technology, the majority of it on hardware: laptops, desktops, and increasingly, tablets. In April 2016, Amazon signed a $30 million contract with New York City Schools for e-books. Forecasts see these investments continuing to increase significantly in coming years as teaching practices embrace technology more. Student access to technology — ranging from web-based resources to the ability to study and write code – is generally seen as an important and positive change for students; technology enables better learning processes and outcomes.
However, schools often deploy technology in hopes it will make classrooms more efficient or save money. All too often, schools don't use the introduction of technology as a way to also rethink their approach to teaching and learning. As a result, "efficiency" becomes a primary driver, whether that is the efficiency of handing in homework, of checking papers for plagiarism, of grading work, or of proctoring exams. The list goes on.
Technology also plays a major role at Quest Forward Learning. However, when we began developing Quest Forward Learning, instead of asking how technology could make teaching and learning more efficient, we asked how teaching and learning could be made more personal, more relevant, more engaging, and more skills-oriented. Then we asked how technology could support that shift.
Rather than framing our mission in terms of efficiency, we focus on methodology and outcomes. This has led us to a range of new discoveries, as well as a unique, innovative learning ecosystem — all based in technology.
Our own Quest Forward Platform, used by learners and mentors on tablets and computers, is central to enabling personalized, active, and engaged learning. Our Quest! app encourages and supports discovery by letting learners choose the quests they want to work on, and then serving up quest-specific resources — web sites, documents, videos, together with guiding reflection questions. Our app does not support traditional, lecture-focused instruction. Instead, it urges learners to work and think on their own, to discover insights, and to shape their own opinions.
In addition, quests are designed to be relevant to the learner's lives. We write quests locally, with deep contextual richness. Our QuestMaker™ app is now used by over 100 curriculum designers in East Africa, Central America and the US to create locally relevant and engaging quests.
Quest Forward Learning avoids certain features that are typically emphasized in education technology, such as multiple choice tests or quizzes. Instead, assessment is based on self-reflection and mentor feedback on authentic work. We also do not offer "adaptive learning" tools, where the software selects the work learners need to do. We intentionally focus both learners and their mentors on understanding and planning their own learning pathway.
Many education technology companies try to scale effective learning by automating more and more of the educational process. As a result, the human touch is removed from learning. At Quest Forward Learning, we believe that we can scale effective learning by putting more agency into the hands of learners, which allows teachers to spend more time mentoring.
We believe that technology, when placed in the right role, can create more personalized, active and engaged learning, and make a tremendous difference in the future of education and the future of our learners.
Manuel Mattke
Manuel serves as Opportunity Education's President and COO. He drives the implementation of Mr. Ricketts's vision for Quest Forward Learning, leads the growth of the Quest Forward Learning Platform, and manages program implementations and support operations.
Previous Article: Q&A with Quest Forward Mentor Brandon Taylor


12 Feb Use bash shell function inside PS1 variable. .. There are total of hacks in this book that will help you build a strong and this eBook. Bash Hacks - Free ebook download as PDF File .pdf), Text File .txt) or read book online for free. 16 Nov Bash Hacks is a downloadable eBook that contains practical examples on both wget -r team-avocats.com http://url-to-webpage-with-pdfs/.
1 Aug Bash Hacks Ebook Pdf Hit team-avocats.com Bash Hacks Ebook Pdf Hit SePage 77 and Sed and Awk Hacks The. Bash Hacks is a downloadable eBook that contains practical examples on various advanced Bash command line and shell scripting features that will. 12 Feb I'm happy to announce the release of my first Free eBook — Linux Hacks. There are total of hacks in this book that will help you build a.
Follow the 3 easy steps mentioned below to get PDF version of Linux Hacks that you will receive, where it says: "Linux Hacks eBook Password: ****** in Linux; Bash Hacks eBook - Take Control of Your Bash Command Line. 8 Aug "Linux Hacks" by Ramesh Natarajan is available in PDF format for free. This book Use bash shell function inside PS1 variable; Hack 26 Jul comMore eBooks from The Geek StuffBash HacksWhen. Linux Hacks team-avocats.com and Awk HacksIf you are. Unofficial guide to ethical hacking torrent land rover discovery 2 td5 rave manual. Bash shell scripting nagios monitoring openssh iptables firewall Network team-avocats.com command line and shell scripting features that will make your Linux journey more.
hacks allows you to take control of your bash command line and shell scripting. discount is offered, when you purchase all three hacks ebooks bash, sed and awk, and vim. Download free collection of 50 hacking ebooks in pdf. 20 Oct There are total of hacks in this book that will help you build a strong Chapter Bash Scripting; Chapter System Monitoring and Performance. Downloads: Read it online (2nd edition). Read it online. Download pdf. Knowledge is not one man's Entity Book Hacked by Read more about hacks, contains, index Sed and awk hacks . Linux Hacks - Free eBook - Parent Directory Lead4pass Latest Lpi Dumps PDF Questions And Answers. 8 Nov More cd examples: 6 Awesome Linux cd command Hacks. gzip command .. 5. Linux Hacks 2nd Edition eBook .. them, I can't copy/paste from the resulting PDF into a notes document. . Bash Hacks eBook.
10 Sep 15 Best Useful Free Linux Ebooks in PDF For Newbies by Pro Hacker . Download – Shell Scripting: Expert Recipes for Linux Bash There are total of hacks in this book that will help you build a strong foundation in. 11 Jan From this website, you can also download the HTML or PDF version of .. Bash Hacks eBook - Take Control of Your Bash Command Line. Wizard crown hacks. linux vim pdf free bash script ebook swing wizard Bingo bash hack tool hacks ebook pdf google apps vim free advanced. A list of best and useful free Linux Tutorial Ebooks to become a power and expert user. All the mentioned Linux Tutorial e-books originally come with a pdf version, This book shares in-depth knowledge about bash scripts, environment , GNU . Linux Hacks – Practical Examples to build a strong foundation on Linux.


You are providing your consent to Epson Australia Pty Ltd. Epson has reports from many customers who have used third party paper and have been very disappointed with the results. Bottom Line A great all-rounder for those on a budget. Economy mode produces very light grey text suitable for proofreading, while draft mode produces slightly darker text that is very blocky. Please try again later. Software Operating System Support. The printer can also produce borderless prints at up to A4 size.
All other names and company names used herein are for identification purpose only and may be the trademarks or registered trademarks of fpson respective owners. All print samples shown herein are simulations. Printing Max Printing Resolution.
Researchers find way to track 'untraceable' 3D-printed guns The 3D-printer leaves a hardware fingerprint. Looking for a tech bargain real soon? Colour photocopies were quite good, though, with plenty of detail, but the colour matching compared to our original document was slightly off.
Epson recommends that primter prints be stored in a photo album or plastic photo storage box in acid free, archival sleeves commonly available from most camera shops. Economy mode produces very light grey text suitable for proofreading, while draft mode produces slightly darker text that is very blocky.
Bottom Line A great all-rounder for those on a budget. The computer environment we test under is as follows: Printers by Rick Broida Oct 16, epso Copying Max Copying Speed.
Headphones by David Carnoy Dec 17, The CX distinguishes itself by having four individual ink cartridges rather than one black and one tri-colour. Overview Specs Consumables Downloads. Epson recommends that you do not use any non genuine printing papers if you sytlus to get the best results from your Epson printer.
Sign in with LinkedIn Sign in with Facebook. Epson is the registered trademark of Seiko Epson Corporation.
Epson Stylus CX – multifunction printer color Sign in to comment Be respectful, keep it civil and stay on topic. The CX is a very flexible document printer and allows for up to four quality modes to be selected: Printers Epson Stylus CX – multifunction printer color.
The printer may not function properly or at all if you use third party ink cartridges. Equipment supplied by Epson Australia is designed to function in conjunction with genuine Epson consumables and accessories specifically configured for it. Max Copying Speed Color.
Unfortunately, this model does not ship with any OCR software. Its photo quality output was excellent during our tests, with no noticeable banding and realistic colour tones.
Warning to Epson printer owners. Input tray – sheets. Discussion threads can be closed at any time at our discretion.


text:
This is Fabrik
Home » Los Angeles » Event » Events » Exhibition » Elijah Pierce and Leroy Almon at The Good Luck Gallery
Elijah Pierce and Leroy Almon at The Good Luck Gallery
Start Date: June 9, 2018
Hours: Opening Reception: June 9, 7-10pm Gallery hours: Wed-Sun 12-6pm
Location: 945 Chung King Road, Los Angeles, CA, USA
A farmer guides a plow behind his stoic mule, three men cheat at cards, a snake with rhinestone eyes slithers through the grass, and enslaved men and women hunch over their labor in the fields under the watchful eye of a blond overseer. The Good Luck Gallery is honored to partner with Just Folk and Cavin-Morris Gallery for an historic exhibition of master African-American woodcarvers Elijah Pierce (1892-1984) and Leroy Almon (1938-1997) opening June 9, 2018.
Two significant twentieth century folk artists, Elijah Pierce and Leroy Almon each grew up in the Southern United States but would make their homes and their marks in Columbus, Ohio. Each would use his craft to further his religious and social mission, with Pierce serving as mentor to the younger Almon.
Elijah Pierce, the son of a former slave, was born in Baldwyn, Mississippi into a deeply religious family. At the age of sixteen he opened a barbershop, and after many years straining against his religious upbringing, finally embraced his traditionalist Christian vocation. He became a minister while continuing to carve and barber, with each practice serving and supporting the other two.
While animals and domestic scenes remembered from his childhood continued to appear in Pierce's work, he also expertly conveyed stories, sermons, and his own deeply personal spiritual history in the form of carved wood panels. It was into this tradition that Leroy Almon was indoctrinated. Born in Tallapoosa, Georgia, Almon met Elijah Pierce and began his work as a wood carver in adulthood. At various times a shoe salesman, Coca-Cola employee, and police dispatcher, Almon too, would eventually find his vocation as a minister. Many of his relief wood carved panels reflect his religious proclivity, exploring themes ranging from famous historical subjects, slavery, and racism, to gambling and promiscuity.
Both artists gained recognition within their lifetimes, though Pierce was in his seventies by the time museums and collectors began to take note. In 1972 Pierce was shown in the Members' Penthouse of The Museum of Modern Art and in 1982 he received the National Heritage Fellowship from the National Endowment of the Arts, following his inclusion in Black Folk Art in America, 1930–1980 at the Corcoran Gallery of Art in Washington, D.C.
Serving as an invaluable record of twentieth-century America, Almon and Pierce's carvings are in the permanent collections of the Smithsonian American Art Museum and the California African American Museum, among others, and were featured in The High Museum's exhibition A Cut Above: Wood Sculpture from the Gordon W. Bailey Collection 2016. Carvings of tigers, hippos, and snakes unite with bas-relief carved story panels in this timely exhibition that explores identity, community, popular culture, and religion in powerful, personal style.
"God speaks to me. I know his voice. 'Elijah, your life is a book, and every day you write a page, and when you are done you won't be able to deny it because you wrote it yourself.'"
-Elijah Pierce, Elijah Pierce Woodcarver, Columbus Museum of Art, 1992
Reception: June 9, 7-10pm
"Parallel Storms" Works by Janie Geiser
1206 Maple Ave, Los Angeles, CA 90015, USA
April 21, 2018 To May 19, 2018
Track 16 is pleased to present an exhibition of Janie Geiser's multifaceted works of video projections, photography, and animatronics. Read more…
Superchief Gallery LA presents Bunnie Reiss "Space Angels"
739 Kohler St, Los Angeles, CA 90021,
November 4, 2017 To December 2, 2017
Superchief Gallery LA is pleased to present the exhibition of Space Angels, a new body of work by Bunnie Reiss, known for her vibrant murals, featuring over… Read more…
Mariah Garnett's "Other & Father" at ltd los angeles
7561 Sunset Blvd #103, Los Angeles, CA
March 12, 2016 To April 16, 2016
ltd los angeles is pleased to announce Other & Father, Mariah Garnett's first solo exhibition with the gallery. Read more…
Event Listing Calendar
No event available
Art Fairs & Festivals
Fabrik Guide
Fabrik Guide provides a comprehensive resource of news and events in the contemporary art and design worlds and a unique insight into the industry. With a comprehensive calendar of events, prominent search bar, and a free weekly newsletter, finding local events in your neighborhood will be easier than ever before.
© 2017 Fabrik Media, Inc. All Rights Reserved.


text:
Music, Film and Theatre
Adamsdown
Butetown
Cyncoed
Danescourt
Ely & Caerau
G-Q
Gabalfa
Leckwith
Lisvane
Llandaff
Llanishen
Maindy
Morganstown
Pentwyn
Pentyrch
Penylan
Pontcanna
Rumney & Llanrumney
Roath
Roath Park and Cyncoed
Radyr
Rhiwbina
Tongywnlais
Whitchurch
Home > Where You Live > City > Cardiff-London rail line electrification costs rise by £1.2bn
Cardiff-London rail line electrification costs rise by £1.2bn
SOARING costs and poor management may see the electrification of the rail line between Cardiff and London cost taxpayers even more, MPs have heard.
A committee of MPs savaged the Great Western Line railway scheme, describing it as "a stark example of how not to run a major project".
The Public Accounts Committee report attacked the project for a "staggering and unacceptable increase in the estimated costs of the Great Western Main Line electrification programme which rose by £1.2 billion in the space of a year".
The committee report states that "it is not clear whether the Great Western electrification project can be delivered to the revised target of December 2018 and budget of £2.8 billion."
The original plan was for the line to be completely electrified at a cost of £1.6 billion. The revised estimate of £2.8 billion does not take into account an accepted risk of losing a further £274 million, £49 million more than the £225 million set aside for contingencies.
Mark Carne, chief executive of Network Rail, was quoted in the report as saying that "every single part of the programme is absolutely on the limit".
The Department for Transport announced in November 2016 that not all of the line would be electrified by December 2018.
Four stretches of track around Bristol, Oxford and the Thames Valley would be "deferred" until the 2019-2024 period.
Work to extend the electrification to Swansea has been delayed until 2024 at the latest. The department defended these decisions, arguing that commuters would feel the benefits of electrification anyway.
The committee responded: "The department's claim that many of the passenger benefits of electrification can be obtained without electrifying the whole route raises questions about whether full electrification is the most appropriate way to achieve benefits for passengers, and value for money for taxpayers."
The report alleged serious problems at almost every step of the project. By the time work had started "the initial design was incomplete, the cost estimating was not good enough and it had started construction before it had the necessary permits and consents."
It clarified that "Network Rail [failed] to put in place an adequate plan to obtain 1,800 separate consents it needed from local authorities."
The report also accused the department of "[failing] to challenge Network Rail's plans effectively, despite the very significant sums of public money at risk."
The department was revealed as being "liable to pay up to £400,000 per day to lease trains that could not be used until the overhead electrification was complete."
Meg Hillier, chairman of the PAC, said: "Mismanagement of the Great Western programme has hit taxpayers hard and left many people angry and frustrated.
"This is a stark example of how not to run a major project, from flawed planning at the earliest stage to weak accountability and what remain serious questions about the reasons for embarking on the work in the first place.
"The sums of public money wasted are appalling — not least the £330 million additional costs the Department for Transport will have to pay to keep the trains running because of delays to electrification.
"The department failed to adequately challenge Network Rail's plans to carry out the infrastructure work and, even now, casts doubt on whether electrification work on this and other lines is even necessary.
"The Government accepts it got this project badly wrong and must now demonstrate it has learned the lessons.
"Network Rail admits there are still very significant risks in the Great Western scheme and it is vital these are fully identified and carefully managed."
Carne explained. "The modernisation of the Great Western line was always going to be a hugely complex job on the world's oldest long distance railway.
"Yet in 2009 it was committed to, then started long before the scale of the work needed was properly understood.
"The industry has learnt painful lessons and future projects will be planned with more rigour and discipline because of this experience."
Appearing on the BBC's Good Morning Wales, committee member and MP for Islwyn Chris Evans admitted there were concerns there would not be enough money to continue with the planned electrification of the Valley Lines.
"The question has got to be asked why are people so angry with the railways, it is quite simple.
"You see them pouring money like this down the drain while rail fares are going up all the time and they are sitting on crowded trains.
"If I was the department and Network Rail, I would be extremely embarrassed by this."
budget, cardiff, commute, commuting, Delayed, Department, Electric, Electrification, Great Western Railway, Line, london, network rail, Overspend, Public, rail, Taxpayer, train, transport
Community order for man who pulled out pistol in GPs' surgery
Lottery funding gives boost to Grange Gardens pavilion
New train to London awaits approval to launch in May 2021
Where Cardiff Council is investing £256m to tackle homelessness
Storm Jorge floods bring train line closures to South Wales
Cardiff Council Tax hike means extra £54.60 per year on your bill


I work under the BACP Ethical Framework.
As part of the service I offer, I believe it is important to have an agreement between counsellor and client.
Please find my contract and other important documents by clicking on this link.
Note: the fees found in these contracts will be revised regularly. If you find a discrepancy or an outdated fee/item, please let me know.
It can be daunting to attend to your first counselling session, but I would like to encourage you to do so anyway if it feels like the right thing to do. Sometimes the first step is the hardest, but you will find it is worth it to go through it. Once in the room, we can take things at your own pace, without judgement or pressure whatsoever. After all, it is your treatment and we are going be kind, compassionate, empathic and understanding all the way through. You set the pace and also, you decide when to end.
Letters and Reports: £30 each.
Fees will change at my discretion, with two months notice to current clients.
Sessions are 50 minutes long. Length of treatment can be short-term, time-limited, or open-ended, depending on your needs.
Cancellations should be made with at least 24 hours notice, otherwise I will need to charge for the missed session. If you choose to not attend your session without cancelling, that session will also be charged at the regular rate.
To ensure the safety of all parties involved, any harm to yourself, myself, others, or children being involved will be disclosed further, after a discussion with you in session. I am legally bound to report terrorism and money laundering. This is the only time that confidentiality might be breached.
If a client comes into the counselling room under the influence of drugs or alcohol, I might need to stop the therapy and offer a session the following week, when the client is no longer intoxicated. I don't believe any fruitful work will be done whilst under the influence of any substance, as it inhibits the ability to engage with the therapeutic process.
Everything discussed in the counselling room is confidential. For professional reasons, I will be keeping notes, which will remain safely in my office at all times. I take notes in a password protected word document in a password protected laptop that is solely for my use.
Please have a look at my Privacy Statement and Cookies Policy for more information on what happens to the data I hold about you.


text:
Stacy Lewis hits from the tee on the 14th hole during the first round of the LPGA Kraft Nabisco Championship.
Na Yeon Choi, of South Korea, watches her tee shot on the 11th hole during the first round of the LPGA Kraft Nabisco Championship.
Anna Nordqvist, of Sweden, tees off on the fifth hole during the first round of the LPGA Kraft Nabisco Championship.
Angel Yin hits from the rough on the second hole during the first round of the LPGA Kraft Nabisco Championship.
Lydia Ko, of New Zealand, is silhouetted as she hits from the tee on the 12th hole during the first round of the LPGA Kraft Nabisco Championship.
Michelle Wie watches her tee shot on the 11th hole during the first round of the LPGA Kraft Nabisco Championship.
Michelle Wie makes a putt on the 12th green during the first round of the LPGA Kraft Nabisco Championship.
Lydia Ko, of New Zealand, right, and Michelle Wie wait to hit on the 11th hole during the first round of the LPGA Kraft Nabisco Championship.
Jodi Ewart Shadoff, of England, hits to the 15th green during the first round of the LPGA Kraft Nabisco Championship.
Momoko Ueda, of Japan, watches her shot on the third hole during the first round of the LPGA Kraft Nabisco Championship.
Ai Miyazato, of Japan, watches her putt on the second hole during the first round of the LPGA Kraft Nabisco Championship.
For Choi, accuracy played a big role in the day's round. She missed just one fairway, and says that's a result of talking to her swing coach after the Kia Classic about focusing on every shot.
"Today I really tried to focus 100 percent with every shot, and then, I mean, after the round I didn't have any regret," she said.
PLEASANT SURPRISE: Angel Yin, just 14, can now say she has led in a major championship. Yin was 2 under after her first two holes Thursday morning, which briefly took her to the top of the leaderboard.
Yin, who averaged 246 yards off the tee and hit seven fairways on her way to a 1-over 73, missed the first two fairways of the day but put her approach shot to just inside 10 feet on both holes. On her way to the third tee, Yin took a peek at the scoreboard, noticed her name on top, then tried to forget what she had just seen.
"Being an amateur, I qualified to play in this, and I didn't expect to play so well," she said. "So seeing myself on the leaderboard for the first time was just really exciting. I was afraid I would mess it up."
This is Yin's second LPGA event, after last year' U.S. Women's Open at Blackwolf Run in Kohler, Wis., and she has learned to "treat it as a normal tournament." Yin had her struggles at the end of the day, making double bogey out of a bunker at the par-3 17th, then putting an aggressive drive into the water at No. 18. The 17th offered another learning experience.
"I was teeing off and I heard a roar and I didn't step (off)," she said. "I should have done that; I should have went back and did my routine again."
HAPPY ANNIVERSARY: This year's Kraft marks the one-year anniversary of Austin Ernst's first professional tournament. At this time last year, Ernst had won an NCAA individual championship, yet had never teed it up in an LPGA event. Playing as an amateur, she opened with 77, came back with 70 to make the cut, then closed with rounds of 68-77 for a T-49 finish.
Ernst, 21, had two birdies and two bogeys Thursday, but lost ground with a double bogey at No. 9 after hitting her approach at the par-5 long and ending up behind a tree. She shot 74.
Ernst turned professional over the summer and earned her card at LPGA Q-School. She has played three events this season and has made the cut every time. Last year, Ernst had father Mark on the bag, but this year she's using veteran tour caddie Tony Lingard as a permanent looper.
NO REASON TO PANIC: World No. 1 Stacy Lewis double-bogeyed her fourth hole of the day, but rebounded for a 1-over 73.
Lewis said it was "a strange day," during which she found a few divots, spent much of the day between clubs and didn't trust her swing.
"This course, you're never really out of it," said Lewis, who won in 2011. "You can shoot a good number one day and be right there. I just kind of had to fight through it a little bit today."
KORDA REUNION: Even Jessica Korda sometimes has to do a double take when she sees her father Petr, a former tennis star, approaching.
"I haven't seen (my parents) since January, and they both came off the plane here, and I was like, 'Oh, my God. You guys are so tall,'" said Korda, who stand 5 feet, 11 inches.
Korda, who opened with a 2-under 70, has played every event this season, and as her face becomes more familiar on this tour, she is asked to give more of her time. Since winning last year's season-opening Australian Open, Korda says she has played every pro-am since. This week she drew celebrity partners Craig T. Nelson and Joel Gretsch.
That Australian victory just happened to coincide with a change of travel plans. Korda spent 2011, her rookie year, traveling with her dad. The Kordas decided to try a different setup at the beginning of 2012. Korda now travels alone, but frequently rooms with Jodi Ewart Shadoff. It's allowed her to figure things out for herself.
"It just works better that way," she said. "You kind of figure out a little bit who you are and what you like. As a junior player, you depend so much on your parents. … It was kind of nice to figure things out your own way."
THE NEXT GENERATION OF SPANISH SPICE: A common comparison between college events and LPGA events is the increased yardages that await on tour. Florida sophomore Camilla Hedberg, from Spain, shrugs that right off.
"My dad is caddieing for me, and the other day I told him I think some of the courses we play in college are longer than this one," said Hedberg, who opened with 72. "The rough is way tougher on this one, but I don't think it plays any longer."
The biggest surprise? Mission Hills' noise level.
"I already expected it to be big and so many people, but I think seeing it and hearing everyone really was a little bit of a surprise."
https://golfweek.usatoday.com/2013/04/04/kraft-notes-pettersen-all-smiles-after-opening-66/
Tiger explains why he chewed gum in Masters win
Geoff Shackelford
AUGUSTA, Ga. – Add gum to the Tiger Woods lore.
Until Sunday in Augusta, Woods had never won a major coming from behind. And now the 2019 Masters champion has won his first major chewing gum from beginning to end.
"Well, I'm chomping on this gum because I usually get hungry, I keep eating so much, and it curbs my appetite a little bit, which is nice," Woods said. "Most of the time, most of the issues I have at tournaments, I lose so much weight, as you all know."
A quibbler might point out that chewing gum should help with him...
Masters: Everything gets 'weird' for Bryson DeChambeau, who shoots 66-75
Steve DiMeglio
AUGUSTA, Ga. – Bryson DeChambeau could have been forgiven if he had refused to meet with the media Friday after his second round in the Masters.
Just a few hours earlier he was leading the tournament, having reached 7 under. He was two shots clear of many of the game's best players and all looked right in his world. And then it didn't.
A bogey at No. 9 when his approach sailed the green, a double at 10 when his chipping deserted him, a bogey at 12 when his tee shot came up short. In four holes, he went from 2...
At Amen Corner, a (power walking) race to best seats in the house during Masters
David Dusek
AUGUSTA, Ga. – If you want to watch the Wimbledon finals from the best seats at Centre Court, become friends with the chairman of the All England Lawn Tennis and Croquet Club. He's the person responsible for handing out invitations to the Royal Box, where Kate and Meghan sit when they attend the oldest major championship in tennis.
At Augusta National Golf Club, site of this week's Masters, the most coveted viewing area is not only open to the public, but it's also organized and governed by the patrons themselves.
Every morning when the gates open at 8 a.m. and fans...
More Uncategorized
Best drivers of 2022 for every budget and handicap
Ian Woosnam announces he's not playing in the Masters anymore
Photos: 2022 The American Express at PGA West and La Quinta Country Club
Golfweek's Best 2021: Best public golf courses you can play, state by state
Golfweek's Best 2021: Best private golf courses in every state
© Copyright Golfweek 2022
App and FAQs
Road to Grayhawk blog


Our expert heating specialists will be able to find the best baxi boiler for you today call us today to order your baxi boiler this industry leading boiler producer will ensure your home is heated to the highest quality. Great customer service, always willing to assist, thorough, professional why would you use any other plumbing company?!? :)". Touchstone energy® cooperatives is a national network of electric cooperatives across 46 states that provides resources.


With UPF 50 sun protection, you've come to know Sungrubbies products, the UV Umbrella is great for travel, beach, walk, hikes, simply being outdoors and for everyday use. This umbrellas provides the sun protection you want and need. With a 43" arc, this double vented umbrella allows wind in to keep you cool without your umbrella blowing away. This product also comes with a lifetime warranty against breakage. It also features an auto open and close button which makes this Umbrella lightweight, easy to carry and operate and reliable. This UV umbrellas has an Ergonomic handle designed to offer a comfortable grip. The umbrella is also water repellant and can be used in the rain. The fact that it's vented, helps with windy days. Finally, this umbrellas is easily foldable, and it folds down to 12.5" and weighs 13 oz.