text:
\section{Introduction}

The cosmological constant problem is usually described as a huge difference between the vacuum energy density derived by quantum field theories and the observed value of the cosmological constant. The energy density associated to the vacuum fluctuations of free fields is a divergent quantity, and any natural cutoff we use to regularize it (for example, the Planck mass or the energy scale of the quantum chromodynamic (QCD) phase transition, the latest cosmological vacuum transition) leads to values many orders of magnitude above the observed $\Lambda$. But the applicability of flat-spacetime quantum field theory in the expanding universe is doubtful, since a non-vanishing bare cosmological constant is not compatible with a flat spacetime.
The vacuum contribution to (semi-classical) gravity is only properly calculated when one considers a non-flat background and renormalizes the divergent contributions in some appropriate way. This is a difficult task and, in general, may depend on the renormalization method used. In the simpler case of free conformal fields in a de Sitter spacetime \cite{H4}, the renormalized vacuum density is proportional to $H^4$, where $H$ is the Hubble parameter. In the high-energy limit this result can be used to obtain a non-singular cosmology, with an initial quasi-de Sitter phase, giving origin to a subsequent radiation dominate period \cite{Tavakol,Carneiro}. However, in the present universe the above result leads to a very tiny vacuum term. On the other hand, it may well be possible that the observed cosmological term is just a cosmological constant of purely geometric nature. In this case there would be no natural (micro-) physical scale associated to it. Furthermore, both the gravitational action of the quantum vacuum and the approximate coincidence between such a constant and the present matter density (the cosmic coincidence problem) would remain unexplained.

As long as this issue cannot be solved on a fundamental level, (semi-) phenomenological models which avoid the theoretical difficulties pointed out above may help to get further insight into the problem.  In this letter we argue that, by modeling the cosmological "constant" in terms of a decaying vacuum energy, it is possible to obtain a model which is competitive with the standard one from the observational point of view.
A crucial point here is to consider the contribution of interacting fields to the vacuum energy. Indeed, some authors have been arguing that the energy density associated to the QCD vacuum condensate in a low-energy de Sitter (or approximately de Sitter) spacetime is given by
\begin{equation} \label{Schutz}
\Lambda \approx m^3 H,
\end{equation}
where $m \approx 150$ MeV is the energy scale of the QCD phase transition \cite{QCD}. In the present universe this density is dominant when compared to the contribution of free fields, $H^4$, and has the correct order of magnitude of the observed cosmological term.
In this paper we will trace back this scaling law $\Lambda\propto H$ to a process of matter production in the expanding spacetime.

\section{Particle production and the vacuum density}

Let us consider a low-energy, spatially flat Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) spacetime, where non-relativistic dark particles of mass $M$ are created out of the vacuum at a constant rate $\Gamma$. The particle number balance (sometimes called Boltzman equation) for this process will be given by
\begin{equation} \label{Boltzman}
\frac{1}{a^3}\frac{d}{dt}\left(a^3n\right)= \Gamma n,
\end{equation}
where $n$ is the particle number density at a given time. It can be rewritten as
\begin{equation} \label{conservacao}
\dot{\rho}_m + 3H\rho_m = \Gamma \rho_m,
\end{equation}
where $\rho_m = nM$  is the matter density. This equation is characteristic of models with interaction in the dark sector \cite{winfried,Chimento,delCampo,Sola}.

This particle production from vacuum fluctuations necessarily involves a gravitational backreaction. In addition to equation (\ref{conservacao}) we have the Friedmann equation
\begin{equation} \label{Friedmann}
\rho = \rho_m + \Lambda = 3H^2,
\end{equation}
where $\Lambda$ is the vacuum contribution to the energy density. We shall assume $p_{\Lambda} = - \Lambda$ for the vacuum pressure, admitting, however, $\Lambda$ to be time varying. The total energy density satisfies the conservation equation
\begin{equation} \label{conservacao2}
\dot{\rho} + 3H(\rho +p) = 0,
\end{equation}
provided we take $\Lambda = 2\Gamma H + \lambda_0$, where $\lambda_0$ is a constant of integration, which corresponds to a purely geometric cosmological constant. Since there is no natural (microphysical) energy scale associated to this constant, it is disregarded here. In this way we have
\begin{equation} \label{linear}
\Lambda = 2\Gamma H,
\end{equation}
and equation (\ref{conservacao2}) can be rewritten as
\begin{equation}
\dot{\rho}_m + 3H\rho_m = -\dot{\Lambda}.
\end{equation}

We can see that the particle creation is concomitant with a decay in the vacuum energy density. Equation (\ref{linear}) is the same time variation law (\ref{Schutz}) obtained in a quasi-de Sitter spacetime when the contribution of the QCD condensate is taken into account \cite{QCD}. In this case we have $\Gamma \approx m^3$, where $m$ is the energy scale of the QCD phase transition\footnote{We are using natural units with $8 \pi G = c = \hbar = 1$.}. As discussed in \cite{QCD}, the association of the QCD energy scale with the observed vacuum energy is natural and, in some way, expected, since the QCD confinement, with breaking of chiral symmetry, is the last cosmological vacuum transition we know. The QCD condensate formed after this low energy transition gives, in a de Sitter (or approximately de Sitter) spacetime, the correct value of the cosmological term (see below). Furthermore, owing to the maximal symmetry of the de Sitter background, the condensate pressure is the negative of its energy density, i.e., the same equation of state associated to a cosmological constant.

Dividing equation (\ref{linear}) by $3H^2$, using $\Lambda/(3H^2) \equiv 1 - \Omega_m$ and specifying to the present time (subscripts $0$), we obtain
\begin{equation} \label{rate}
\Gamma = \frac{3}{2} \left( 1 - \Omega_{m0} \right) H_{0}.
\end{equation}
In a de Sitter universe ($\Omega_m = 0$) we would have $\Gamma = 3H/2$. That is, the particle creation rate would be equal (apart from a numerical factor) to the Gibbons-Hawking temperature associated to the event horizon \cite{Gibbons}. On the other hand, by taking $\Omega_{m0} \approx 1/3$ for our present universe, we have $H_0 \approx m^3$ and $\Lambda \approx m^6$. The former relation is an expression of the old Eddington-Dirac large number coincidence \cite{Mena}, while the latter (known as Zeldovich's relation \cite{Bjorken}) gives the correct order of magnitude for $\Lambda$. The exact value of $\Gamma$ in (\ref{rate}) (and hence of $\Lambda_0$) will be given by observations in the next sections. Once $\Gamma$ is fixed, no further fine-tuning will be necessary. The cosmological model
to be built will have the same number of free parameters as  the  $\Lambda$CDM model, namely $\Omega_{m0}$ and $H_0$.

\section{The model}

From this section on we will analyze the cosmological model arising from a vacuum energy density scaling with time in accordance with the ansatz discussed above. When compared with the most precise observational constraints, the model will show a very good concordance and, in some cases, less tensions than in the standard case. Therefore, besides providing a possible physical basis for the cosmological term, in the lines of the previous sections, it will also show to be competitive from the observational point of view.

With $\Lambda = 2\Gamma H$ we obtain, from the Friedmann equations, the solution \cite{Humberto,Jailson}
\begin{equation}\label{Hgeral}
\frac{H}{H_0} \approx \left\{ \left[1 - \Omega_{m0} + \Omega_{m0} (1
+ z)^{3/2}\right]^2 + \Omega_{r0} (1+z)^4 \right\}^{1/2}\;,
\end{equation}
where $\Omega_{m0}$ is the present relative matter density, and we have added conserved radiation with present density parameter $\Omega_{r0}$. As discussed in \cite{Jailson,Jailson2,Jailson3}, for non-zero $\Omega_{r0}$ the expression (\ref{Hgeral}) is an approximate solution, differing only $1\%$ from the exact one, since $\Omega_{r0} \approx 8 \times 10^{-5} \ll 1$. For $\Omega_{r0} = 0$, the solution (\ref{Hgeral}) is exact.

For early times we obtain $H^2(z) = H_0^2 \Omega_{r0} z^4$, and the radiation era is indistinguishable from the standard one. On the other hand, for high redshifts the matter density scales as $\rho_m(z) = 3H_0^2 \Omega_{m0}^2 z^3$. The extra factor $\Omega_{m0}$ - as compared to the $\Lambda$CDM model - is owing to the late-time process of matter production. In order to have nowadays the same amount of matter, we need less matter in the past. Or, in other words, if we have the same amount of matter in the past (say, at the time of matter-radiation equality), this will lead to more matter today. We can also see from (\ref{Hgeral}) that, in the asymptotic limit $z \rightarrow -1$, the solution tends to the de Sitter solution.

Note that, like the $\Lambda$CDM model, the above model has only two free parameters, namely $\Omega_{m0}$ and $H_0$. On the other hand, it can not be reduced to the $\Lambda$CDM case
except for $z\rightarrow -1$. In this sense, it is falsifiable, that is, it may be ruled out by observations.

\section{Background tests}

The Hubble function (\ref{Hgeral}) is all we need to test the model against observations of SNIa and BAO \cite{Jailson,Jailson2,Jailson3}. However, when testing the position of the first peak of the CMB anisotropy spectrum, some care is needed. The relation between the observed position of the peak and the acoustic scale $l_A$ is given by \cite{Tegmark}
\begin{equation}\label{l1}
l_1 = l_A (1 - \delta_1), \quad  \mbox{where} \quad \delta_1 = 0.267 \left( \frac{r}{0.3} \right)^{0.1},
\end{equation}
with $r \equiv \rho_r/\rho_m$ evaluated at the redshift of last scattering $z_{ls}$. The acoustic scale is defined, as usual, by
\begin{equation}\label{lA}
l_A = {\pi \int_0^{z_{ls}}
\frac{dz}{H(z)}}/{\int_{z_{ls}}^{\infty}\frac{c_s}{c}\frac{dz}{H(z)}},
\end{equation}
with the sound velocity
\begin{equation}\label{cs}
c_s = c \left( 3 + \frac{9}{4}\frac{\Omega_{b0}}{z\Omega_{\gamma 0}}
\right)^{-1/2},
\end{equation}
where $\Omega_{b0}$ and $\Omega_{\gamma 0}$ stand for the present density parameters of baryons and photons, respectively. The relation (\ref{l1}) does not depend on the dark energy model, but only on pre-recombination physics. However, the ratio $r$ is, in our case, given by
\begin{equation} \label{r}
r = \frac{\Omega_{r0}}{\Omega_{m0}^2} z_{ls},
\end{equation}
with the extra factor $\Omega_{m0}$ as compared to the $\Lambda$CDM expression. Note that, in all the above expressions, there is a dependence on $H_0$ through the relative densities of baryons, photons and radiation, as well as through the redshift of last scattering. In our analysis we will fix these parameters ($c_{s}$, $\Omega_{r0}$, $z_{ls}$) to the concordance values of the standard model. The only free parameters to be adjusted will then be $\Omega_{m0}$ and $H_0$.

\begin{figure*}
\vspace{.2in}
\centerline{\psfig{figure=MLCS_05.eps,width=2.2truein,height=2.2truein}
\psfig{figure=MLCS_12.eps,width=2.2truein,height=2.2truein}
\psfig{figure=mlcs2k2joint.eps,width=2.2truein,height=2.2truein}}
\caption{{\bf Left panel:} superposition of the confidence regions from SDSS (MLCS2k2) SNIa, BAO and the position of the first peak of the CMB in the present model \cite{ Jailson3}. {\bf Center panel:} the same for the spatially flat $\Lambda$CDM. {\bf Right panel:} The corresponding likelihoods when $h$ is marginalized.}
\label{figsdss}
\end{figure*}

The result of a joint analysis of SNIa, BAO and the position of the first peak of the CMB spectrum is shown in Figure \ref{figsdss}. In the left panel we show the superposition of the corresponding confidence regions in the ($h$,$\Omega_{m0}$) plane, where $h = H_0/100$(km/s)/Mpc is the dimensionless  Hubble constant. The central panel shows the same for the $\Lambda$CDM model. In the right panel a comparison between the two models is made, after marginalizing over $h$. In this analysis we have used the SDSS SNIa compilation with the MLCS2k2 light-curve fitter \cite{SDSS}. Other current compilations make use of Salt or Salt2 fitters which, however, are not model independent. A more complete analysis, including the Union2 and Constitution compilations, can be found in \cite{Jailson3}. In the case of the Constitution sample calibrated with MLCS2k2, the results are very similar to those presented here. Note that for the standard model the relative matter density is higher than the usually accepted concordance value ($\Omega_{m0}\approx 0.27$). This is a characteristic of the MLCS2k2 fitter, also present when we use it to calibrate the Constitution sample.

\begin{figure*}[]
\vspace{.2in}
\centerline{
\psfig{figure=espectro.eps,width=2.2truein,height=2.15truein}\hspace{.6in}
\psfig{figure=mlcsA.eps,width=2.2truein,height=2.2truein}}
\caption{{\bf Left panel:} the 2dFGRS power spectrum in the present model with $\Omega_{m0} = 0.45$ (blue solid line) and for the BBKS transfer function with $\Omega_{m0} = 0.27$ (red line). {\bf Right panel:} superposition of the four tests (SNIa, BAO, CMB and LSS) performed with the present model. The blue ellipse corresponds to the concordance region.}
\label{figpowersp}
\end{figure*}

\section{The matter power spectrum}

The analysis of the matter power spectrum was performed in Ref. \cite{Julio}, where, for simplicity, baryons were not included and the cosmological term was not perturbed. In a subsequent publication a gauge-invariant analysis, explicitly considering the presence of late-time non-adiabatic perturbations, has shown that the vacuum perturbations are indeed negligible, except for scales near the horizon \cite{Zimdahl}. Therefore, the result of Ref. \cite{Julio} can be considered a good approximation. An updated analysis is shown in the left panel of Figure \ref{figpowersp}, together with the 2dFGRS data points \cite{2dF} and, for comparison, the concordance $\Lambda$CDM fitting as provided by the BBKS transfer function \cite{BBKS}. It is also shown the $2\sigma$ confidence region for our fitting.

\section{Joint analysis}

\begin{table}[t]
\begin{center}
\caption{Limits to $\Omega_{m0}$ (SNe+ CMB + BAO+LSS).}
\begin{tabular}{rcccc}
\hline \hline \\
\multicolumn{1}{c}{ } & \multicolumn{2}{c}{$\Lambda(t)$CDM } & \multicolumn{2}{c}{$\Lambda$CDM } \\
\multicolumn{1}{c}{Test}&
\multicolumn{1}{c}{$\Omega_{m0}$\footnote{Error bars stand for $2\sigma$}}&
\multicolumn{1}{c}{$\chi^2_{min}/\nu$}&
\multicolumn{1}{c}{$\Omega_{m0}$$^a$}&
\multicolumn{1}{c}{$\chi^2_{min}/\nu$}\\ \hline \\
Union2 (SALT2)......&$0.420^{+0.009}_{-0.010}$ & 1.063 & $0.235\pm 0.011$ & 1.027 \\
SDSS (MLCS2k2).......& $0.450^{+0.014}_{-0.010}$ & 0.842 & $0.260^{+0.013}_{-0.016}$ & 1.231 \\
Constitution (MLCS2k2[17]).......& $0.450^{+0.008}_{-0.014} $ &1.057 & $0.270\pm 0.013$ & 1.384\\
\hline \hline
\end{tabular}
\end{center}
\end{table}

In the right panel of Figure \ref{figpowersp} we show the superposition of the $1\sigma$ and $2\sigma$ confidence regions for the four tests we are considering here (SNe Ia, BAO, first peak of CMB and LSS), as well as the concordance ellipses of our joint analysis. The concordance value for the matter density is $0.44 < \Omega_{m0} < 0.46$ ($2\sigma$). The Hubble parameter is smaller than in other estimations, but it has the same value obtained when the same SNIa sample is analyzed for the $\Lambda$CDM model (see Fig. \ref{figsdss}). In what concerns the matter density parameter, it is about $10\%$ higher than the flat standard model value for the SDSS (MLCS2k2) compilation ($\Omega_{m0} \approx 0.40$). In both models the obtained values of $\Omega_{m0}$ are higher than the usually accepted concordance value for the flat $\Lambda$CDM model, and the same occurs when one uses the Constitution sample calibrated with MLCS2k2. A discussion about the present tension between different SNIa samples and fitters, in both models, can be found in \cite{Jailson3}. Here we show, in Table I, the best-fit results for $\Omega_{m0}$ (with $h$ marginalized) with three samples of supernovas: the SDSS and Constitution calibrated with the MLCS2k2 fitter, and the Union2 (which is calibrated with SALT2). In Figure \ref{figure03}, on the other hand, the reader can find the evolution of the scale factor (left panel) and of the relative energy densities of radiation, matter and dark energy (central and right panels) in the two models.

The concordance value obtained for $\Omega_{m0}$ is in agreement with estimates based on peculiar velocity measurements for galaxy pairs \cite{galaxies}, but only in marginal agreement with dynamical estimations from clusters \cite{clusters}. It is important to emphasize, however, that such estimations are not very precise and that they involve a different scale.
Note also that the present result has an approximative character. As discussed in \cite{Julio}, the inclusion of baryons in the analysis of the power spectrum may lead to a difference of about $10\%$ in the estimation of $\Omega_{m0}$.

With the concordance values of $h$ and $\Omega_{m0}$ in hand, we can obtain the age of the Universe, as well as the redshift of transition between the decelerated and accelerated phases. They are given, respectively, by \cite{Jailson}
\begin{equation} \label{idade}
H_0t_0 = \frac{2\ln\Omega_{m0}}{3(\Omega_{m0}-1)} ,
\end{equation}
and
\begin{equation} \label{transicao}
z_T = \left[2\left(\frac{1}{\Omega_{m0}}-1\right)\right]^{2/3}-1.
\end{equation}
This leads to $H_0 t_0 = 0.97$ and $z_T = 0.81$, in good agreement with standard predictions and astronomical limits \cite{age}. For $h \approx 0.7$ we have $t_0 \approx 13.5$ Gyr.

\begin{figure*}[]
\vspace{.2in}
\centerline{
\psfig{figure=figure03.eps,width=6.4truein,height=2.5truein}}
\caption{{\bf Left panel:} The time evolution of the scale factor in the spatially flat $\Lambda$CDM and in the present model. {\bf Center panel:} The density parameters of matter and dark energy in both models. {\bf Right panel:} The density parameters of matter and radiation in both models. In all cases we are using the best-fit values of $\Omega_{m0}$ from the SDSS analysis, and the density parameters are defined as $\Omega_i = \rho_i(z)/3H^2(z)$.}
\label{figure03}
\end{figure*}

\section{The CMB anisotropy spectrum}

It is not easy to perform a full analysis of the CMB anisotropy spectrum with alternative models, specially if it involves new processes like particle production, for example. Nevertheless,
for at least some of the features
we do not expect significant changes.
First of all, radiation and baryons are assumed to be separately conserved (there is no photon fluctuations from the vacuum at the tree level, and baryons are too heavy to be produced at late-times). Therefore, the CMB temperature, the acoustic horizon at the last scattering and the relative height of the peaks will not be affected.

On the other hand, the redshift of equality between matter and radiation in our model is given by
\begin{equation} \label{igualdade}
z_{eq} = \frac{\Omega_{m0}^2}{\Omega_{r0}},
\end{equation}
where we can note again an extra factor $\Omega_{m0}$ as compared to the standard $\Lambda$CDM result. By using our concordance matter density $\Omega_{m0} = 0.45$, we obtain $z_{eq} \approx 2500$, which does not differ too much from the standard value. (This is simply because $0.25 = 0.5^2$. Therefore, a relative matter density of around $0.5$ in the present model leads to the same $z_{eq}$ of the standard model with $\Omega_m \approx 0.25$). For this same reason, the matter density at the time of equality will be approximately the same in both models. [By the way, this result for $z_{eq}$ guarantees that the turnover of the matter power spectrum is correctly placed (see Fig. \ref{figpowersp} and \cite{Julio})]. As the redshift of last scattering is exactly the same \cite{Jailson2}, and the recombination does not depend on a particular dark energy model, both last scattering and recombination will occur in the matter dominated phase. All these results indicate that the absolute height of the peaks will not change either.\footnote{In reference \cite{chineses} the authors claim, by using an adapted version of CAMB, that a good fitting for the CMB spectrum can be obtained with our concordance matter density, $\Omega_{m0} \approx 0.45$ (see the left panel of their Figure 3). On the other hand, they claim that this density leads to a matter power spectrum in disagreement with LSS data, contrary to what we have obtained in \cite{Julio}. Our present results, however, agree with those obtained previously in reference \cite{Julio}.}

\begin{figure*}[]
\vspace{.2in}
\centerline{
\psfig{figure=juntos2A.eps,width=2.2truein,height=2.15truein}\hspace{.6in}
\psfig{figure=potenciais.eps,width=2.2truein,height=2.15truein}}
\caption{{\bf Left panel:} the density contrast as a function of redshift for the Einstein-de Sitter solution (blue), the spatially flat $\Lambda$CDM model with $\Omega_m = 0.27$ (yellow) and the present model with $\Omega_m = 0.45$ (red), for the same initial condition $\delta \approx 10^{-5}$ for $z = 1100$. {\bf Right panel:} the corresponding gravitational potential as a function of $z$, for $k=0.002\,h/$Mpc.}
\label{figdcontrast}
\end{figure*}

The only important consequence of matter production on the CMB spectrum could be owing to the integrated Sachs-Wolf effect (ISW).
In the right panel of Figure \ref{figdcontrast} we plot the gravitational potential $k^2\Phi = \rho_m a^2 \delta/2$ ($\delta$ is the matter density contrast and $k$ is the comoving wavenumber) as a function of the redshift, for the Einstein-de Sitter, $\Lambda$CDM and $\Lambda(t)$CDM models, for $k=0.002\,h/$Mpc. The ISW effect is  proportional to the integrated change of the gravitational potential. As the right panel of Fig.~\ref{figdcontrast} shows, the slope of the potential of our model differs from the corresponding slope of the $\Lambda$CDM model. But also here one may expect this effect to be small. In the $\Lambda$CDM model the potential decreases by $24$\% between the
last scattering and the present time, in our $\Lambda(t)$ model
it decreases by $20$\%. Note, however, that Fig.~\ref{figdcontrast} is preliminary since it is based on a Newtonian analysis \cite{Julio}. Here, a more quantitative, fully relativistic analysis is necessary.

On the other hand, as can also be seen in Fig.~\ref{figdcontrast}, there is a small difference in the gravitational potential as compared to the standard model, a difference that will affect the normalization of the CMB spectrum, since the Sachs-Wolf effect is proportional to $\Phi$. But the gravitational potential is proportional to the  matter density contrast as well. Therefore, if the latter is correctly normalized (by using, for example, the BBKS transfer function \cite{BBKS}, as was done, e.g., in \cite{Julio} and in the left panel of Fig.~\ref{figpowersp}), the CMB spectrum will also have the correct normalization. In other words, in order to have the correct normalization today, we have more power in the CMB spectrum at high redshifts as compared to the standard case.

\section{The coincidence problem}

The coincidence problem within the $\Lambda$CDM model is usually phrased as: why $\rho_{m}$ and $\Lambda$
are of the same order of magnitude just at the present epoch? Our model relies on dark-matter particle production at a constant rate. From the outset, this rate is a free parameter. By Eq.~(\ref{rate}) it is assumed here to be of the order of the Hubble constant. For our model the coincidence problem translates into: why the rate $\Gamma$ is of the order of the present-time Hubble rate $H_{0}$ (and not of the order of the Hubble rate at a different time)? Any other value of $\Gamma$ would not be compatible with the observed cosmological dynamics.

Compared with the $\Lambda$CDM model, the coincidence problem is alleviated, however, in the sense that $\Omega_{m}/\Omega_{\Lambda} \propto a^{-3/2}$ \cite{Zimdahl}, whereas in the $\Lambda$CDM model one has $\Omega_{m}/\Omega_{\Lambda} \propto a^{-3}$. Any decay of the ratio $\Omega_{m}/\Omega_{\Lambda}$ that is less than $a^{-3}$ can be considered as an alleviation of the coincidence problem \cite{dalal}.

This difference in the background dynamics also influences the behavior of the perturbations. As the left panel of Fig.~\ref{figdcontrast} shows, the present model deviates from an Einstein-de Sitter universe already at higher redshifts than the $\Lambda$CDM model. Moreover, while the perturbations within the latter approach a constant value for decreasing $z$, in our model there appears a maximum around the present epoch and perturbations are suppressed for $z \rightarrow -1$.

\section{Conclusions}

The origin and nature of the dark sector is probably the central theoretical problem of modern cosmology. The non-zero tiny value of the cosmological term and its coincidence with the matter density are some important faces of the question. Relating dark energy with vacuum fluctuations is an old difficulty, but one may expect a potential solution if this problem is appropriately considered in curved spacetime. Several models of dynamic vacuum have been suggested along these lines. Models for  accelerated expansion based on matter creation in the expanding background have previously been proposed, e.g., in \cite{winfried,Ademir}. Although a relation between dynamical dark energy and particle production is not mandatory, we think it represents an interesting option.

This paper is based on the assumption that the late-time spacetime expansion can extract non-relativistic particles from the quantum vacuum. In the case of a constant creation rate, the backreaction of this process leads to a vacuum density linearly proportional to the Hubble parameter, a result previously obtained from estimations of the gravitational contribution of the QCD vacuum condensate. The resulting cosmological model is shown to be in accordance with the most precise observational tests, namely those which involve SNIa, the anisotropy spectrum of the CMB, the LSS distribution and BAO, albeit for higher values of the current matter density than in the standard model. Another difference to the $\Lambda$CDM model may be a modified ISW effect. This will be a subject of future research.

\section*{Acknowledgements}

This work was partially supported by CNPq and FAPERJ.

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Alkem Laboratories Ltd. to Launch State of the Art Technology for Diabetic Foot Ulcer Management
Alkem Laboratories Ltd. | January 13, 2022
Alkem Laboratories Ltd. (Alkem) hereby announces to launch a unique patented technology for the treatment of Diabetic Foot Ulcer (DFU) in India. The solution would be based on disruptive 4D Bioprinting technology, which would be used to treat deep, non-healing chronic wounds and is expected to be launched in the Indian market in the latter half of 2022 post regulatory approval. This advanced technology for DFU management has a high scope of preventing amputations in diabetic patients. This technology will be available at affordable rates to Indian patients at a time when there is no definitive treatment for DFU in India. India currently has approximately 77 mn diabetes patients, the second highest in the world. A diabetic foot ulcer is one of the most significant and devastating complications of diabetes and is defined as a foot affected by ulceration that is associated with neuropathy and/or peripheral arterial disease of the lower limb in a patient with diabetes. Approximately, 12-15% with diabetes suffer from DFU at least once in a lifetime. 5–24% of them will finally lead to limb amputation within 6–18 months after the first evaluation. The risk of foot ulceration and limb amputation increases with age and the duration of diabetes. Alkem has collaborated with Rokit Healthcare Inc. to commercialize the technology in India to help reduce amputation amongst DFU patients considering the negative impact of amputation on a patient's quality of life and the associated economic burden on the healthcare system. "In India, Diabetes is one of the major healthcare challenges. The challenge in itself is so huge that diabetic foot ulcers often get ignored. Approximately 1 lac people have to undergo amputation every year and compromise on their quality of life. To address the problem, Alkem has collaborated with Rokit Healthcare Inc., a global regenerative solutions company, to bring out novel solutions for the management of diabetic foot ulcers." Mr. Sandeep Singh, Managing Director, Alkem Laboratories Ltd Adding further, Mr. Sandeep asserted, "Alkem, over the years, has always been at the forefront in delivering high-quality patient care, through its innovation and patient-centric initiatives." About Alkem Laboratories Ltd Established in 1973 and headquartered in Mumbai, Alkemis a leading Indian pharmaceutical company with global operations, engaged in the development, manufacture, and sale of pharmaceutical and nutraceutical products. The Company produces branded generics, generic drugs, active pharmaceutical ingredients (APIs), and nutraceuticals, which it markets in India and International markets. With a portfolio of more than 800 brands in India, Alkem is ranked the fifth largest pharmaceutical company in India in terms of domestic sales. The Company also has presence in more than 40 international markets, with the United States being its key focus market.
Texas Children's Hospital And Baylor College of Medicine COVID-19 Vaccine Technology Secures Emergency Use Authorization In India
Texas Children Hospital | December 29, 2021
Texas Children's Hospital and Baylor College of Medicine announced today that CORBEVAX™, a protein sub-unit COVID-19 Vaccine, whose technology was created and engineered at its Center for Vaccine Development (CVD), has received Emergency Use Authorization (EUA) approval from the Drugs Controller General ofIndia(DCGI)to launch inIndiawith other underserved countries to follow. Dubbed "The World's COVID-19 Vaccine", it uses a traditional recombinant protein-based technology that will enable its production at large scales making it widely accessible to inoculate the global population. The initial construct and production process of the vaccine antigen was developed at Texas Children's Hospital CVD, led by co-directors Drs. Maria Elena Bottazzi and Peter Hotez and in-licensed from BCM Ventures, Baylor College of Medicine's integrated commercialization team, to Hyderabad-based vaccine and pharmaceutical company Biological E. Limited (BE). CORBEVAX™ after completing two Phase III clinical trials involving more than 3000 subjects was found to be safe, well tolerated and immunogenic: CORBEVAX™ demonstrated superior immune response in comparison with COVISHIELD™ vaccine when assessed for Neutralizing Antibody (nAb) Geometric Mean Titers (GMT) against the Ancestral-Wuhan strain and the globally dominant Delta variant. CORBEVAX™ vaccination also generated significant Th1 skewed cellular immune response. CORBEVAX™ nAb GMT against Ancestral-Wuhan strain is indicative of vaccine effectiveness of >90% for prevention of symptomatic infections based on the Correlates of Protection assessment performed during Moderna and Astra-Zeneca vaccine Phase III studies. CORBEVAX™ nAb GMT against the Delta strain indicates a vaccine effectiveness of >80 percent for the prevention of symptomatic infections based on published studies. While none of the subjects who took CORBEVAX™ or COVISHIELD™ had serious adverse events, CORBEVAX™ had 50 percent fewer adverse events than COVISHIELD™. In the continuous monitoring of phase II studies, CORBEVAX™ showed high persistence of immune response as indicated by <30% drop in nAb GMT till 6 months second dose as compared to >80% drop observed with majority of the vaccines. "Protein-based vaccines have been widely used to prevent many other diseases, have proven safety records, and use economies of scale to achieve low-cost scalability across the world," said Dr. Maria Elena Bottazzi, Professor and Associate Dean of the National School of Tropical Medicine at Baylor and Co-Director of the Texas Children's Hospital Center for Vaccine Development. "Our decade-long studies advancing coronavirus vaccine prototypes has led to the creation of this vaccine, which will fill the access gap created by the more expensive, newer vaccine technologies and that today are still not able to be quickly scaled for global production." The need for safe, streamlined, low-cost vaccines for middle- to low-income countries is central to the world's fight against the COVID-19 pandemic. Without widespread vaccination of populations in the Global South, additional virus variants will arise, hindering the progress achieved by currently available vaccines in the United States and other Western countries. "This announcement is an important first step in vaccinating the world and halting the pandemic. Our vaccine technology offers a path to address an unfolding humanitarian crisis, namely the vulnerability the low- and middle-income countries face against the delta variant," said Dr. Peter Hotez, Professor and Dean of the National School of Tropical Medicine at Baylor and Co-Director of the Texas Children's Hospital Center for Vaccine Development. "Widespread and global vaccination with our Texas Children's-Baylor-BE vaccine would also forestall the emergence of new variants. We have previously missed that opportunity for the alpha and delta variant. Now is our chance to prevent a new global wave from what might follow." "Over the years, we have worked to make quality vaccines and pharmaceutical products accessible to families around the world. With this as our backdrop, we resolved to develop an affordable and effective COVID-19 vaccine. It has now become a reality. We deeply appreciate Texas Children's Hospital Center for Vaccine Development, Baylor, CEPI, the Bill and Melinda Gates Foundation, and the government of India for their continuous support and cooperation during this journey. The combined efforts & unceasing support demonstrate that we can collectively overcome any challenge". Mahima Datla, Managing Director, Biological E. Limited ABOUT TEXAS CHILDREN'S HOSPITAL Texas Children's Hospital, a not-for-profit health care organization, is committed to creating a healthier future for children and women throughout the global community by leading in patient care, education and research. Consistently ranked as the best children's hospital in Texas, and among the top in the nation, Texas Children's has garnered widespread recognition for its expertise and breakthroughs in pediatric and women's health. The hospital includes the Jan and Dan Duncan Neurological Research Institute; the Feigin Tower for pediatric research; Texas Children's Pavilion for Women, a comprehensive obstetrics/gynecology facility focusing on high-risk births; Texas Children's Hospital West Campus, a community hospital in suburban West Houston; and Texas Children's Hospital The Woodlands, the first hospital devoted to children's care for communities north of Houston. The organization also created Texas Children's HealthPlan, the nation's first HMO for children; has the largest pediatric primary care network in the country, Texas Children's Pediatrics; Texas Children's Urgent Care clinics that specialize in after-hours care tailored specifically for children; and a global health program that's channeling care to children and women all over the world. Texas Children's Global Health program leads efforts that advance health care equity through innovative collaboration in care, education and research for underserved populations globally. Texas Children's Hospital is affiliated with Baylor College of Medicine. ABOUT TEXAS CHILDREN'S HOSPITAL CENTER FOR VACCINE DEVELOPMENT Texas Children's Hospital Center for Vaccine Development is one of the leading vaccine development centers in the world. Established in Washington DC as the Sabin Vaccine Institute Product Development Partnership (PDP) in the year 2000 and after relocating to the Texas Medical Center in 2011, it rebranded as Texas Children's Center for Vaccine Development. For the past two decades it has acquired an international reputation as a non-profit PDP, advancing vaccines for poverty-related neglected tropical diseases (NTDs) and emerging infectious diseases of pandemic importance. In addition, it builds and strengthens capacity for vaccine development locally and with foreign nations and leads global efforts to guide and influence vaccine policy and advocacy through "vaccine diplomacy" as an international bridge for peace and vaccine development capacity. ABOUT BCM VENTURES Baylor College of Medicine Ventures is the commercial engine of the health sciences university, created to support the translation of academic knowledge and intellectual assets for the benefit of society. We do this by engaging university innovators, entrepreneurs and industry to fully develop ideas along their best commercial path. We foster a culture of commercialization and engage with industry to identify market opportunities for collaborative ventures. ABOUT BIOLOGICAL E. LIMITED Biological E. Limited (BE), a Hyderabad-based Pharmaceuticals & Biologics Company founded in 1953, is the first private sector biological products company in India and the first pharmaceutical company in Southern India. BE develops, manufactures and supplies vaccines and therapeutics. BE supplies its vaccines to over 100 countries and its therapeutic products are sold in India and the USA. BE currently has 8 WHO-prequalified vaccines in its portfolio. In recent years, BE has embarked on new initiatives for organisational expansion such as developing generic injectable products for the regulated markets, exploring synthetic biology and metabolic engineering as a means to manufacture APIs sustainably and developing novel vaccines for the global market.
L2Mtech GmbH Receives CE Mark Approval on 6(SIX) products for Cardiovascular and Endovascular Applications
L2Mtech | February 17, 2021
CE Mark Approval for LimusTrack™, Sirolimus Eluting Coronary Stent System for Cardiovascular Applications. CE Mark Approval for LomiFlow™, Paclitaxel Drug Eluting Balloon for Cardiovascular Applications CE Mark Approval for PearlFlow™, Paclitaxel Drug Elutin Balloon for Endovascular Applications CE Mark Approval for PearlFlow NS™, Self Expandable Nitinol Stent System for Endovascular Applications CE Mark Approval for FlexiTrack 018™, Peripheral Balloon Catheter for Endovascular Applications CE Mark Approval for FlexiTrack 035™, Peripheral Balloon Catheter for Endovascular Applications Bonn, Germany – L2Mtech GmbH has announced the award of its first CE Mark approval on Six (6) products: LimusTrack™ : Sirolimus Coated Cobalt Chromium Stent with biodegradable polymer for the treatment of coronary artery disease, de novo lesions, restenosis lesions. LomiFlow™ : Paclitaxel Coated balloon catheter for the treatment of coronary artery disease, small vessels, dilatation of de novo lesions, in-stent restenosis (ISR) cases. PearlFlow™ : Paclitaxel Coated balloon catheter for the treatment of peripheral arterial disease, PTA, dilatation of stenotic segments or lesions in peripheral arteries. PearlFlow NS™ : Self-Expanding Nitinol Stent System for the treatment of peripheral arterial disease, de novo lesions, lesions in femoropopliteal arteries. FlexiTrack 018™ : Peripheral Balloon Dilatation catheter for the treatment of peripheral arterial disease, dilatation of lesions in femoral, popliteal, tibial arteries. FlexiTrack 035™ : Peripheral Balloon Dilatation catheter for the treatment of peripheral arterial disease, dilatation of lesions in the SFA, femoral arteries. L2Mtech GmbH Founder and CEO Lalit Mamtani said ''We are very excited to have been awarded our first CE Mark on six products, CE Mark approval represents a key milestone for L2Mtech GmbH and is a testament to the efficacy and safety of our innovative technology products for Cardiovascular and Endovascular applications." We now prepare to commercially launch the products in all markets where the CE Mark is recognized. With introduction of our innovative technology products in markets, we will be able to expand treatment options for the benefit of many millions of patients with coronary and peripheral artery disease around the world. About L2Mtech Founded in 2017, L2Mtech GmbH is a privately-owned multinational medical device company headquartered at Bonn, Germany. L2Mtech specializes in design, development, manufacture and commercialization of medical devices that are used by healthcare establishments globally. L2MTech will provide interventional physicians with innovative vascular devices including Drug Eluting Balloon manufactured in Europe.Our Core mission is to build a product portfolio focused on minimally invasive treatment for patients with cardiovascular,endovascular and vascular artery disease. For further information, please visit : L2MTech.de Media Contact: L2Mtech GmbH admin@L2Mtech.de +49 228 94730761
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Friendly firewalls
9 Sep 2013 ~ Jon Udell
In Schneier as a technology leader Dave Winer reacts to this comment about SOAP made by Bruce Schneier at the 2002 Emerging Technology conference: "SOAP is a firewall-friendly protocol like a bullet is skull-friendly." I'm pretty sure that was the quote because I jotted it down in the notes I took that day. It's funny how things change. Back then, during the first flush of excitement about web services, SOAP was how the tech industry imagined web services would talk to one another. And REST was, as it still is, how in most cases they actually do talk to one another.
If REST had SOAP's approval rating back then, Schneier might as easily have said: "REST is firewall-friendly like a bullet is skull-friendly." That would have been equally true. And equally irrelevant. Because as it turns out, enabling web services to tunnel "securely" through HTTPS is the least of our concerns. If governments have compromised the endpoints, and/or the encryption protocol itself, all bets are off.
In Dave Winer's notes from that 2002 talk he wrote:
Jon Udell, who I respect enormously said that Schneier was the leading authority on security. My impression, and it's just an impression, is that this kind of praise has gone to his head.
Dave's recollection of that conference is accurate. Bruce was snarky. He did bash Microsoft. He also put forward the visionary idea that we can best secure computer networks by managing risks the way the insurance industry does. That was a conclusion he reached after fundamentally rethinking his own long-held assumptions about the capabilities and relevance of cryptography. In my review of his book Secrets and Lies, which describes that intellectual journey, I wrote:
It's a rare book that distills a lifetime of experience. It's a rarer one that chronicles the kind of crisis and transformation that Bruce Schneier has undergone in the last few years. He's emerged with a vital perspective. Cryptography is an amazingly powerful tool, but it's only a tool. We need to use it for all it's worth. But at the same time we have to be clear about its limitations, and locate its use within a real-world context that is scarier and more complicated than we dare imagine.
The people I most respect nowadays are those who can change their minds in response to new information and changing circumstances. In 2000, when Secrets and Lies was published, we didn't dare imagine that our worst adversaries were elements of our own governments. Now that we know that's true, can Bruce Schneier help lead the way forward? I hope so. And while I agree that a snarky attitude can be a problem, if deployed carefully in the right context — say, a congressional hearing — it might come in handy.
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A friend, posting to facebook, puzzled over his own perception of an exceptionally gifted artist of the surface of things being hailed as an artist of deep psychological penetration. I suggested he hold his original perception. There is no doubt that our age assumes you can see with realism, that seeing must be best without sentiment, that only the objective, penetrating gaze will do. This is the illusion of our age.
In truth, you see truly only with love.
I am struck by the difference between Stanley Spencer's haunting nudes of himself and Patricia Preece - freed into their utter honesty by a seeing love - and Freud's that are earnest, intense, brilliantly executed and hauntingly superficial.
Meanwhile, it was another artist that occupied my weekend: Sir William Nicholson. He will, I expect, slowly come to occupy a place as one of England's finest artists of the first half of the last century, a place shared with Spencer - artists in a radically different mode yet sharing a loved vision of things, resting in joy.
I stayed with a friend on Friday who regularly visits his daughter whose ninetieth birthday it was that day. In mentioning her visit, I was reminded of the art: beautiful in its accomplished stillness, allowing things to stand forth in their innate poetry, as actually loved and thus known. Nicholson knew that you can paint surfaces only if you see through the object with love, that the surfaces can only live if you caress the depths.
It is the lesson that violence never learns.


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Rongbuk Monastery
West side of east of Rongbuk Ditch which under the foot of south of Mt. Everest, Basong Village, Tingri County, Shigatse, Tibet
Temple with local characteristics.
Rongbuk Monastery was built by a local Lama in 1899. Because it is located at the north slope of the Mt. Everest, 5,154 m above the sea level. It is the base camp for mountaineers and an ideal location to view Mt. Everest from afar. Walking forward from Rongbuk Monastery, you will also see the famous Rongbuk Glacier Zone, which is the largest among hundreds of glaciers formed around the Mt. Everest.
Climbers must pass through Rongbuk in order to reach the highest peak of Mt. Qomolangma via the North Face. It has been described as having some of the most dramatic views in the world, presenting a panorama of the Shishapangma, Mt. Qomolangma, Cho Oyu, and Gyachung Kang peaks to visitors.
In previous times, the monastery became very active with the teachings at certain times of the year. It was, and is, the destination of special Buddhist pilgrimages where annual ceremonies are held for spectators coming from as far as Nepal and Mongolia. These ceremonies were shared with the satellite monasteries across the Himalaya also founded by the Rongbuk Lama.The Rongbuk Monastery built up according to the mountain, a total of five floors, using only two floors. It is said that why the monastery built so high was because it was quiet here, easy to have a rest. People here believe in Nyingma. The Marnyi stone under the white pagoda outside the monastery is local Buddhist believers pray for good luck for themselves. The main hall of Rongbuk Monastery enshrined the Buddha sakyamuni and padmasambhava. Buddhist monks and nuns live together in the monastery and to carry out Buddhist practice activities. It its flourishing period there were more than three hundreds of monks and three hundreds of nuns, more than 20 halls.
Rongbuk Monastery is the base camp from the North Slope to climb Mt. Everest. Overlooking the south from here, you can see the Mt. Everest like a giant pyramid, stands tall in the mountain peaks, daunting. Whenever the weather is sunny, people can see a milky white cloud in the top of the mountain, like the white flag flying in the Mt. Everest, referred to as "the world's highest banner cloud", which is a great wonder of the world.
Sooner or later there will be strong winds, the temperature can be as low as 15 to 20 degrees below zero (from December to March), it is best to take warm clothes. From April to October, along the road there are tents that can be accommodate, each bed about 30 to 40 yuan/person. During the tourist season from May to August there will be a situation that it is hard to find a tent to stay.
Every April 15th in Tibetan Calendar, there will be three-day sorcerer's dance in a trance activity, and on Tibetan calendar 29 November there will hold a grand ceremony of exorcism. It is said that April 15th in Tibetan Calendar was the day that Buddha Sakyamuni born, enlightened, and parinirvana. Therefore in this month people will hold all kinds of activities to commemorate, over time these activities become grand scale circumambulation as the main activity of the festival.
Rongbuk Monastery is a monastery of Nyingma Sect that both the monks and nuns live together in the monastery. The old Rongbuk Monastery is 3 kilometers away from the south of the new Rongbuk Monastery which is closer to Mt. Everest. There are still relics related to Master Padmasambhava since he cultivated himself here.
The new Rongbuk Monastery was finished construction in 1902. It had more than ten branches of monasteries (some of them were in Nepal) in its heyday. It has eight affiliated monasteries today, including a nunnery. Rongbuk Monastery is only about 20 kilometers away from the top of Mt. Everest and it has been the base camp for mountaineers climb the peak from the northern slope.
Rongbuk Glacier
The Rongbuk Monastery was built according to the mountain, and the Rongbuk River at the foot of Rongbuk Monastery is the ice water river collected from the three glaciers of northern slope of Mt. Everest—East Rongbuk Glacier, Middle Rongbuk Glacier and West Rongbuk Glacier. There are 15 glaciers which covers an area of more than 10 square kilometers, among which the largest one is Rongbuk Glacier. Rongbuk Glacier is 26 kilometers long with an average thickness of 120 meters. It is more than 300 meters at its thickest. Upon glaciers there are various and rich rare serac forest, chopped ice, ice bridge, etc. And there are as high as dozens of meters of ice cliffs, the trap of light and shade ice cracks, and avalanche of dangerous area.
【Qiangmu Dance】
Qiangmu, also called "sorcerer's dance", is a kind of religious dance. Each April 15th of Tibetan calendar is the festival to commemorate Sakyamuni birthday. And Qiangmu will be held in the next day. In that day, there are many tents stationed in the Rongbuk Monastery, villagers who come to see Qiangmu staying here one day in advance.
Most of the Tibetans who come to watch Qiangmu Dance bring with butter tea and zampa. At ten o'clock, the Qiangmu Dance of day officially starts. First by the monks with yellow cockscomb pulled open the prelude, the first appearance of Ngawang, slowly turned down along the yard on the left side of the wooden stairs, stood in the yard to knock the cymbals, greeted one after another of the monks down the stairs. In addition to the khenpo, they came on stage according to the age.
【Chinese Name】: 绒布寺
【Recommended Visiting Hours】: 2 hours
【Transport Information】: Going to Rongbuk Monastery people have better to charter a car starts from New Tingri, because there is nearly no free-ride or passenger buses. Rongbuk Monastery is 20 km from the top of Mt. Everest, and 8 km from base camp.
Top Attractions in Shigatse
Tashilhunpo Monastery
Gyantse Dzong
Zhangmu Town
Pelkor Chode Monastery
Shalu Monastery
Pala Manor
Mt. Everest
Mount Everest Base Camp
Recommended Shigatse Tours
6 Days Mystical Tibet Exploring Tour
8 Days Tibet Everest Base Camp Tour
10 Days Travel through Tibet to Nepal


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Color realism is a fine art style where accurately portrayed colors create a sense of space and form. It employs a flattening of objects into areas of color, where the modulations occur more as a result of an object interacting with the color and light of its environment than the sculptural modeling of form or presentation of textural detail. The actual color of an object, or 'local color', is held secondary to how that color interacts with surrounding light sources that may alter the look of the original color. Warm light of the sun, cool light from the sky, and warm reflected light bouncing off other objects are all examples of how a local color may be affected by its location in space.

Earliest proponents of this style include the Dutch Master Johannes Vermeer and Hendrick Terbrugghen.
Recent artists working with this style include the Boston School of painters, such as Edmund Tarbell and William McGregor Paxton. These artists combined vibrant Impressionist pastel colors with a more traditional palette, to create color-realist works that have a full range of dark to light values. Contemporary artists utilizing elements of this style include Sam Vokey, Charles Tersolo, and Barbara Glee Lucas.

References

Visual arts genres
Realism (art movement)
Realism

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