text:
New Polar Bear 'Death' Model Based On Junk Science And Climate Porn
By: Admin - Climate DepotJuly 20, 2020 5:48 PM
https://climatechangedispatch.com/new-polar-bear-death-model-based-on-junk-science-and-climate-porn/
Climate Change Dispatch / by Susan J. Crockford / 1h
A prediction that polar bears could be nearly extinct by 2100 (which was first suggested back in 2007) is news today because there is a new model.
As for all previous models, this prediction of future polar bear devastation depends on using the so-called 'business as usual' RCP8.5 climate scenario, which has been roundly criticized in recent years as totally implausible, which even the BBC has mentioned.
This new model, published today as a pay-walled paper in Nature Climate Change, also did something I warned against in my last post: it uses polar bear data collected up to 2009 only from Western Hudson Bay – which is an outlier in many respects – to predict the response of bears worldwide.
The lead author, Peter Molnar, is a former student of vocal polar bear catastrophist Andrew Derocher – who himself learned his trade from the king of polar bear calamity forecasts, Ian Stirling.
Steven Amstrup, another co-author of this paper, provided the 'expert opinion' for the failed USGS polar bear extinction modelfeatured in my book, The Polar Bear Catastrophe That Never Happened.
Well, these authors and their supporters got the headlines they crave, including coverage by outlets like the BBC and New York Times(see below), but I have to say that the combination of using out-of-date Western Hudson Bay information on when polar bears come ashore in summer and leave for the ice in fall (only to 2009) to make vague projections ('possible', 'likely', 'very likely') about all other subpopulations in addition to depending on the most extreme and now discredited RCP8.5 climate scenario (Hausfather and Peters 2020) for this newest polar bear survival model is all that's needed to dismiss it as exaggerated-fear-mongering-by-proxy.
Why would anyone believe that the output of this new model describes a plausible future for polar bears?
Meanwhile, polar bear populations worldwide continue to thrive despite declines in sea ice.
And as I have pointed out on numerous occasions, the ice-free period for WH has not continued to decline since 1998 but rather has remained stable (with yearly variation) at about 3 weeks longer than it was in the 1980s (Castro de la Guardia et al 2017).
Moreover, for the last five years at least, including this one, the ice-free season for WH bears has been better (only 1-2 weeks longer than the 1980s), although no official data on this phenomenon has yet been published.
Oddly, this more recent data for Hudson Bay was not used for the Molnar model.
Also this year, the first polar bears off the ice in Western Hudson Bay are at least two weeks later than they have been in recent years: Andrew Derocher's first tagged bear came to shore 17 July 2020 (see below):
The first tag-free bear spotted onshore at Wakusp National Park south of Churchill by live webcams was caught on film 13 July (see video below and notice how fat it is).
Other photos over the last few days show very fat bears and cubs just off the ice. All of this means that the mean date of all bears off the ice this summer will almost certainly be early August – as late as it was in the 1980s.
The lead author of this new paper (Molnar et al. 2020), Peter Molnar, has written something similar before.
He concocted a model for Western Hudson Bay polar bear survival a decade ago (Molnar et al. 2010) that predicted 28-48% of male polar bears in WH would die if climate change caused the fasting period to be extended from the 120 days (4 months) that were usual during the 1980s to 180 days (6 months) sometime in the future.
A colleague of his put together a similar model generating similar results a couple of years later (Robbins et al. 2012), which I wrote about here.
Here is a quote from the methods that show even their preferred polar bear vs. sea ice data for WH could not be used without fiddling with it because it didn't fit their assumptions of what the bears should be doing (my bold):
"…we assumed that fast duration is linked to the annual number of ice-free days in each subpopulation region. We computed the ice-free season from observed and modelled daily sea-ice concentrations, and linked our estimates to reported annual migration dates of polar bears in the Western Hudson Bay subpopulation to ensure that each year's first and last fasting day were defined from a polar bear's perspective.
The ice-free season was defined as the period when the extent in a subpopulation region is below a critical value. Our choice of this critical extent was based on when polar bears in the Western Hudson Bay subpopulation were observed to arrive on-shore (leaving the ice) in summer and depart the land (returning to ice) in autumn. The migration dates were assessed from bear locations tracked by satellite-linked radio collars in 1991–2009, as reported in ref. 38 [Cherry et al. 2013]. The mean days of the year of bear on-shore arrival and departure to sea ice were 212 [31 July] and 329 [25 November], respectively (averaged across all bears in all available years from 1991–2009; Extended Data Fig. 2). However, according to Extended Data Fig. 1, the mean sea-ice extent in Western Hudson Bay on day 212 was extremely low (3.8% of the annual maximum in the years 1991–2009), suggesting that bears may have lingered on a few persistent clusters of small, highly ridged floes, which could provide cover for aquatic stalks, before giving up on the ice and coming ashore. In contrast, on day 329, the extent was 48.5% of the annual maximum in 1991–2009 in the Western Hudson Bay subpopulation region [i.e. they know bears leave for the ice as soon as its 5-10% ice-covered].
Because ice extent differed substantially between bear arrival and departure dates, we chose one critical extent that is a compromise between the two, and computed times when extent first crosses the critical value for three consecutive days in summer and fall (Extended Data Fig. 1). Then, because the fasting period is defined as the number of days between the bears' on-shore arrival in summer and their departure to sea ice in autumn, we adjusted the days of the year when critical extent is crossed by constant offsets to match the mean observed arrival/departure (and hence fast initiation/cessation) dates in the Western Hudson Bay subpopulation (Extended Data Fig. 2).
In essence, offsets at the start and end of the ice-free season are estimates of how long bears will linger on the last persistent floes after the extent has fallen below the critical value, and of how long it takes the bears to return to the ice after it rises above the critical value. We sought a critical extent that allows a small offset in the autumn (consistent with polar bears eager to get back on the sea ice after a long fast) and a moderate offset in summer (suggesting that polar bears continue on-ice foraging for as long as possible).
Dr. Susan Crockford is a zoologist (former adjunct professor, University of Victoria) specializing in Holocene mammals, including polar bears and walruses. Her new book is called The Polar Bear Catastrophe That Never Happened (Amazon).
Read rest at Polar Bear Science
Filed under: arctic, ice, models, polar bears, species


Long sleeved tops are the perfect basic for your wardrobe.
Long sleeved tops are a genious fashion basic: So chic and versatile! You can either wear them at warm summer nights or on colder days, be it for a walk in the park or a regular day at the office. Promod europe offers you a great variety of long sleeved tops. Prints, rollnecks, glitzy applications and photo motifs are only some of the details that create that unique design of each and every one of our long sleeved tops. You can choose between simple basic tops that go very well with smart trousers and a knit cardigan or, if you prefer a more casual look, you can wear a printed top with weatherbeaten jeans or any chino. A glitzy finish of the fabric rounds off the look and gives it that extra glitzy glam! Either roll up the sleeves or leave them down.
Choose any of our long sleeved tops and experience that French fashion chic! Long sleeved tops by Promod are a pretty addition to your wardrobe!


Industry professionals registered with RECA may use RECA's logo in their advertising. Industry professionals must not include the logo in advertising that is harmful to the best interests of the public, the industry as a whole or RECA.
If RECA receives a complaint about an industry professional improperly or inappropriately using the RECA logo, in a way that breaches these guidelines, it can review their conduct and can sanction in accordance with the Real Estate Act Rules.
Only industry professionals can use the RECA logo in their advertisements. If an unlicensed individual advertises services as an industry professional and includes the RECA logo, this could be an aggravating factor in the case of an unlicensed activity investigation.


Diamond Tower presents an entire wall of winning possibilities and offers a glimpse into the good life. It was designed to present different valuables on its five reels that have 1,024 ways to win with the four rows of symbols showing after each spin. In addition to the wild symbols, the Amaya slot machine has a bonus game from which players can win prizes, free games and multipliers.
The life of the rich and famous has been the topic of slot machines for a long time and Amaya features Diamond Tower as a unique take on the style that presents all sorts of valuable items. Designed by Cryptologic, this 5-reel slot machine with four rows makes for an entertaining gaming experience where winning happens very often. One of the reasons why it is almost difficult to get a non-winning spin is the fact that the Diamond Tower slot machine has 1,024 ways to win, making it possible to get winning combinations with ease. To make the prizes even more impressive, there are wild symbols which are represented by the image of the pretty lady. These can substitute for other symbols in order to create the best prizes. The bonus symbol is the image of a large diamond and 2, 3 or 4 of them scattered left to right will trigger the Hold N Spin phase. This is where the diamond symbols change into locks and cover the entire reel, keeping it in place while the remaining reels spin three times. Another bonus symbol on an active reel will also lock it in and reset the spins to 3 again. If all the reels are locked during the game, the action will move to the Break-In Bonus. This will present a wall with security boxes on six levels. Players must pick a door on the highlighted level in order to get free spins and multipliers. There is also a diamond that is used to advance to the next level for better prizes and an alarm that ends the picks. It is possible to win up to 12 free games and a multiplier of up to x8 from the bonus game. The regular symbols in the game are represented by a luxurious car, a small dog, jewelry and other expensive items, with the addition of six card symbols.


My friend Ashley had a farm themed party for her youngest daughter with a real life petting zoo. She had pony rides with the petting zoo, face painting and a balloon artist, Chick-fil-a and doughnuts for dessert. AKA a kids dream. She is an event planner, after all.
I was fairly surprised that both boys wanted to go into the petting zoo. They both tend to get skittish around animals, even if they are fascinated by them.
James just wanted to hold this dirty brush. Not to actually brush any animal, just to hold it and try to brush his own hair. I had to take this photo fast before i had to swipe his hand away again.
But then Zach and I saw this tiny goat. Could you die? Is he not the cutest thing ever?
And doesn't he look like a real farm kid kneeling to pet it?
Until it got a bit too friendly and knocked him over.
He rebounded fine. And you guys, it was funny seeing your kid get "attacked" by a 2 lb goat. Hilarious.
He also, of course, wanted to get his face painted. But instead of picking a "something" he said he wanted to look like an army man. So she painted camo on his forehead. He looked like a walking bruise. He wanted to get his entire face done, but he had a basketball game that afternoon. I didn't think he needed full camo on his face prior to running up and down the court at the Y.
James refuses to get his face painted. Refuses. He wants nothing to do with it, but will take a balloon sword to hit you across the knees with. Always be on guard.


This weekend, I celebrated 2 years of being in remission. All day long I couldn't stop thinking about how blessed I was to be celebrating another year of life. I was hesitant to celebrate because I'd just had a complete body bone scan done the day before and I had no idea what the results of that test were, but I wanted to move forward and celebrate anyway. The day started out normally with routine Saturday housework. About mid morning, I received a nice surprise from my Texas girl. She'd sent a lovely arrangement of blue delphinium and white roses. She's so thoughtful and her arrangement really set the tone for the day. The blue and white flowers were so peaceful and serene, just the way I needed my day to be.
Early afternoon brought the arrival of my youngest daughter. She'd come to spend the weekend with us and help me celebrate. She's always so full of energy and we had fun catching up on her week and the latest information on her current relationship.
As the day wore on, I took time to look back through my cancer notebook. When I was initially diagnosed, the hospital gave me a nice heavyweight vinyl binder with the words "Love Me...Love My Journey" printed on it. Inside were various dividers for medical bills and expenses, test results, medications, etc. I never thought I'd fill up that notebook, but after 2 years it's overflowing. I've tried to be diligent about recording every doctor visit, every lab test, every medication, every expense, and notes to help my children know what cancer felt like from day one. As I read back through my notes and recounted each event, I couldn't help but marvel at all I'd experienced. The past 2 years had been extremely difficult but I'd managed to make it through. I was proud of that accomplishment.
We began our celebration of my 2nd cancerversary with a family dinner at one of my favorite Chinese restaurants. Although only 2 of my children were able to be present, I was thankful they'd taken time out of their busy schedules to come be with me. My granddaughter, Heather, was such a joy to watch as she tried her best to master chopsticks. We enjoyed a leisurely dinner and ate to our heart's content. We left the restaurant with barely enough room for the dessert I had waiting at home. Earlier in the week, I'd stopped by a local bakery, Smallcakes,and ordered a special treat. They make the most decadent Key Lime cupcakes.
Back at the house, we entered my formal dining room. As soon as we walked in, Heather exclaimed, "HAPPY DAY!!! HAPPY DAY!!!" She's just a little shy of being 3 years old and can't quite say Happy Birthday but she knows what balloons and festive decorations mean...something good is about to happen. We couldn't help but laugh at her sweet, childlike expression of joy. It was indeed a happy day. With my family gathered around, I thanked them for standing by me for the past 2 years. As I began speaking, I was overcome with emotion and had to fight back tears to complete my expression of gratitude to them. The tears came in torrents as each one of them blessed me with their gifts of love. My daughter, Jamie, had written a sweet prayer and had it placed in the Wailing Wall in Jerusalem. My daughter, Laura, had made a photo slideshow on DVD chronicling my journey. I was touched at their thoughtfulness.
I am blessed to be so loved. My heart overflows with gratitude at all I've been given. Yes, I've suffered physical difficulties these past few years but the love of my family has made them much easier to bear. And now I start on this new year of life. I look forward to seeing what God has in store for me in the days ahead. And Heather was right, it was truly a HAPPY DAY!
What a great time of celebration! So happy for you!


Soil water budget in the Trier-Bitburger-Mulde.
Investigation of soil water budget in the unsaturated soil zone is commonly performed for determination of the complex relationships between the different components of the water budget. A main focus of this work was on acquisition and evaluation of percolation water and soil moisture dynamics depending on the site properties (climate, soils, land use). A network consisting of 14 lysimeter and soil moisture measuring stations was established in the region of the Trier-Bitburger-Mulde (SW-Eifel, Germany). During a period of four hydrological years precipitation, infiltration, percolation water and soil moisture were collected weakly on the stations comprising the different regional characteristics of soil textures and land use patterns. The analysis of the weekly data sets enabled to point out seasonal variations of percolation water and soil water dynamics (as time-depth function). Comparison of simultaneously collected data sets of percolation water, soil moisture, and evapotranspiration shows significant fluctuations, which result from the complex relationships between the site properties. Hereby, the soil properties and in particular the secondary macropores (root channels, shrinkage- /frost cracks) have a striking influence on the variability of the water flows in the unsaturated soil zone. The results of the GIS-based regionalisation of the annual amount of percolation water prove the influence of topography (relief conditions, especially slope and aspect) on percolation and soil water dynamics in low mountain ranges.


text:
\section{Introduction}

The standard cosmological scenario, or  $\Lambda$-cold-dark-matter ($\Lambda$CDM) model, is the most accepted model to explain the observable Universe and its late-time accelerated expansion. However, some mild observational tensions among different datasets emerge in this scenario, namely Planck data analyzed within the $\Lambda$CDM model \cite{Planck:2018vyg} show a tension between 4 and 6$\sigma$ with late-time, model-independent measurements \cite{Riess:2019cxk,Wong:2019kwg,BOSS:2014hwf,BOSS:2012dmf,SDSS:2008tqn,Freedman:2019jwv,Yuan:2019npk,Riess:2021jrx} of the  Hubble constant $H_0$ and with weak lensing data for the estimation of the present time amplitude of the matter power spectrum in terms of $\sigma_{8,0}$ \cite{deJong:2015wca}, see also Refs.~\cite{DiValentino:2020vvd,DiValentino:2020zio,DiValentino:2021izs,DiValentino:2018gcu} for general overviews. We can further mention the Planck lensing anomalies about the excess of lensing in the temperature power spectrum \cite{Planck:2018vyg}. Additionally, the cosmological constant, $\Lambda$, responsible for the late-time accelerated expansion, is plagued by theoretical issues, such as (among others) the well known Cosmological Constant Problem \cite{Weinberg:1988cp,Carroll:2000fy,Weinberg:2000yb,Padilla:2015aaa}, i.e.\ the discrepancy between the theoretically predicted value for $\Lambda$ and the observed one, and by the Coincidence Problem \cite{Velten:2014nra}, namely why the magnitude of the energy densities for matter and the cosmological constant are comparable today. These issues are motivating the search for new physics beyond the $\Lambda$CDM model \cite{CANTATA:2021ktz}.

In this paper we specialize on a modified gravity (MG) theory, the Galileon one \cite{Nicolis:2008in,Deffayet:2009mn,Deffayet:2011gz}, whose generalization is equivalent \cite{Kobayashi:2010cm} to the  Horndeski theory \cite{Horndeski:1974wa}. For a long time Horndeski theory has been considered to be constructed from the most general action for a scalar field coupled to gravity that leads to second order equations of motion, but later it has been found that more general actions can be constructed, namely those of the beyond Horndeski \cite{Gleyzes:2014dya} and DHOST \cite{Langlois:2015cwa} theories. The Galileon/Horndeski theory allows for self-accelerating solutions which have been the basis of inflationary scenarios \cite{Kobayashi:2010cm,Burrage:2010cu,Mironov:2019qjt,Creminelli:2010qf,Renaux-Petel:2011rmu,Kamada:2010qe,DeFelice:2013ar,Kobayashi:2011pc,Gao:2011qe,Takamizu:2013gy,Frusciante:2013haa} and late-time explanations of cosmic acceleration \cite{Deffayet:2010qz,Charmousis:2011bf}. The observation of the Gravitational Waves (GW) event GW170817 \cite{LIGOScientific:2017vwq} and of its electromagnetic counterpart GRB170817A \cite{Goldstein:2017mmi}, set a stringent bound on the speed of propagation of GWs \cite{LIGOScientific:2017zic}, which in turn severely constrains the form of the Galileon action \cite{Creminelli:2017sry,Ezquiaga:2017ekz,Baker:2017hug,Amendola:2017orw}, leaving only a sub-class still viable. Within the surviving Galileon models, data analysis with Planck data alone found that $H_0$ is consistent with its local determination respectively at 1$\sigma$ for the generalized cubic covariant Galileon model \cite{Frusciante:2019puu} and at 2$\sigma$ for the Galileon ghost condensate \cite{Peirone:2019aua}, resolving the $H_0$ tension. For the latter, a joint data analysis of cosmic microwave background (CMB) radiation, baryonic acoustic oscillations (BAO), supernovae type Ia (SN) and redshift-space distortions (RSD) showed that it is also statistically preferred over the $\Lambda$CDM scenario due to  suppressed large-scale temperature anisotropies and a peculiar behavior of the scalar field equation of state in the early-time expansion history \cite{Peirone:2019aua}.

In this work, we are interested in a particular class of Galileon models, specifically the one in which the scalar field can give rise to \textsl{scaling solutions}. Scaling solutions \cite{Copeland:1997et,Ferreira:1997hj,Liddle:1998xm,Barreiro:1999zs,Guo:2003rs,Guo:2003eu,Tsujikawa:2004dp,Piazza:2004df,Pettorino:2005pv,Amendola:2006qi,Ohashi:2009xw,Gomes:2013ema,Chiba:2014sda,Amendola:2014kwa,Albuquerque:2018ymr,Frusciante:2018aew,Amendola:2018ltt} are characterized by a constant ratio between the energy density of the matter components and that of the scalar field. In this case, the density of the scalar field is not negligible compared to the other components even at early time, thus the model shows compatibility with the energy scale associated with particle physics. This feature might alleviate the Coincidence Problem since the initial conditions in the scaling regime are fixed by the model parameters.

A general Galileon Lagrangian allowing for scaling solutions has the form $L = Xg_2(Y)-g_3(Y)\Box \phi$ \cite{Frusciante:2018aew}, where $X \equiv - \partial_{\mu} \phi \partial^{\mu} \phi / 2$ and $g_2$, $g_3$ are general functions of  $Y=X e^{\lambda \phi} $ with $\lambda$ being a constant. For this Lagrangian, scaling solutions are also present when the scalar field $\phi$ is coupled to non-relativistic matter with a constant coupling  $Q$ \cite{Frusciante:2018aew}. Concrete models have been proposed for $g_3$, such as $g_3 = a_1 Y + a_2 Y^2$, with $a_1$ and $a_2$ constants, together with an exponential potential and a direct coupling between the scalar field and matter \cite{Gomes:2013ema}, or $g_3 = A \ln Y$, with $A$ being a constant, together with a standard kinetic term and two exponential potentials \cite{Albuquerque:2018ymr}. For the resulting model, the density associated to the $g_3$ term gives important contributions to the field density during scaling radiation and matter eras, but then it is subdominant at later-time relative to the density associated to the standard field Lagrangian characterizing $g_2$.
This feature is  expected to accommodate  the observational data of galaxy and Integrated-Sachs-Wolfe (ISW) cross-correlations, which indeed do not seem to prefer  dominance  of cubic interactions at late-time \cite{Kimura:2011td,Renk:2017rzu,Kable:2021yws}. Furthermore,
the $g_3$ term modifies the gravitational couplings felt by matter and light, leading to a modified evolution of perturbations \cite{Albuquerque:2018ymr}. These signatures can be used to distinguish the model from standard Quintessence and $\Lambda$CDM \cite{Banerjee:2020xcn}. In this work we will investigate this model, to which we will refer to as the Scaling Cubic Galileon (SCG) model. We will provide a thorough analysis of cosmological perturbations and their effects on CMB anisotropies, lensing potential and growth of structures and finally we will present the cosmological constraints obtained using  combinations of data sets.

This paper is organized as follows. In Sec.~\ref{sec:II} we review the theoretical framework of the  SCG model. In  Sec.~\ref{Sec:CosmoObs} we present the theoretical predictions for some cosmological observables.  In Sec.~\ref{Sec:Constraints} we provide the cosmological constraints using the Markov chain Monte Carlo (MCMC) method. Finally we conclude in Sec.~\ref{Sec:Conclusion}.

\section{The Scaling Cubic Galileon Model} \label{sec:II}

In this section we review the SCG  model, whose action reads:
\begin{equation}
\mathcal{S}=\int d^4x\sqrt{-g}\left[\frac{R}{16 \pi G_N}+\mathcal{L}_{\rm SCG}(\phi,X)+\mathcal{L}_{ \gamma}(g_{\mu\nu},\chi_{\gamma})\right]\,,
\end{equation}
where $G_N$ is the Newtonian gravitational constant, $g_{\mu\nu}$ is the metric and $g$ is its determinant, $\mathcal{L}_{\gamma}$ is the Lagrangian of matter fluids, $\chi_{\gamma}$, and $\mathcal{L}_{\rm SCG}$ is the  Lagrangian describing the SCG model, defined as follows \cite{Albuquerque:2018ymr}
\begin{equation}
\mathcal{L}_{\rm SCG}=  X-V_1 e^{-\beta_1 \phi} - V_2 e^{-\beta_2 \phi} - A \ln Y \Box \phi , \label{eq:SCGaction}
\end{equation}
with  $V_1$, $V_2$, $\beta_1$,  $\beta_2$, $A$ and $\lambda$ being constants. $V_1$, $V_2$, $\beta_1$ and $\beta_2$ are positive defined and $\beta_1$ and $\beta_2$ are chosen such that $\beta_1 \gg \mathcal{O} (1)$  in order to satisfy early-time constraints on the field density parameter from Big Bang Nucleosynthesis and  CMB
measurements \cite{Copeland:1997et,Albuquerque:2018ymr}, while $\beta_2 \lesssim \mathcal{O} (1)$ in order to realize the late-time acceleration \cite{Barreiro:1999zs}. The double exponential potential is chosen because it provides the necessary mechanism for the scalar field to exit the early-time scaling regime during which its density is proportional to that of the matter components (hence the name SCG) into a late-time epoch of cosmic acceleration \cite{Albuquerque:2018ymr} (another example in the context of standard Quintessence is Ref.~\cite{ Barreiro:1999zs}). In the following we adopt the unit $8 \pi G_N = 1$.

\subsection{Background Equations}
Let us consider a flat Friedmann-Lemaître-Robertson-Walker (FLRW) background described by the line element
\begin{equation}
    ds^2 = - dt^2 + a^2 (t) \delta_{ij} dx^i dx^j ,
\end{equation}
where $a(t)$ is a time-dependent scale factor. The modified Friedmann equations for the SCG model read
\begin{align}
    3H^2 &= \rho_{\gamma} + \rho_{\phi} , \label{eq:FriedConst}  \\
    2\Dot{H} + 3H^2 &= - \left( p_{\gamma} + p_{\phi} \right) , \label{eq:AccEq}
\end{align}
where $H(t) \equiv \Dot{a}/a$ is the Hubble expansion rate and a dot represents a derivative with respect to cosmic time. The quantities $\rho_{\gamma}$ and $p_{\gamma}$ correspond, respectively, to the energy density and pressure of the standard matter fluids, namely, cold dark matter (c), baryons (b) and photons (r), and are related through the barotropic equation of state $p_{\gamma} = (\gamma - 1) \rho_{\gamma}$.  The constant barotropic coefficient is $\gamma_{\rm b,c} = 1$ for baryons and cold dark matter and $\gamma_{\rm r} = 4/3$ for photons. Additionally, $\rho_{\phi}$ and $p_{\phi}$ are the energy density and pressure of the scalar field $\phi$ defined as
\begin{align}
    &\rho_{\phi} = \frac{\Dot{\phi}^2}{2} + V_1 e^{-\beta_1 \phi} + V_2 e^{- \beta_2 \phi} + 6 H A \Dot{\phi} - A \lambda \Dot{\phi}^2 , \\
    &p_{\phi} =  \frac{\Dot{\phi}^2}{2} - V_1 e^{- \beta_1 \phi} - V_2 e^{- \beta_2 \phi} - 2 A \left( \frac{\lambda \Dot{\phi}^2}{2} + \Ddot{\phi} \right)\, . \end{align}
Finally, the equation of motion for the scalar field is:
\begin{equation} \label{eq:EqMotSF}
    \frac{1}{a^3} \frac{d}{dt} \left( a^3 J \right) = P \,,
\end{equation}
with
\begin{align}
&J= \Dot{\phi} + 6 A H - 2 A \lambda \Dot{\phi}\,,\\
&P=\beta_1 V_1 e^{- \beta_1 \phi} + \beta_2 V_2 e^{-\beta_2 \phi}\,.
\end{align}

It is possible to  rewrite the dynamics of the background evolution of the SCG in terms of the following dimensionless variables:
\begin{equation} \label{eq:SCGVar}
    x = \frac{\Dot{\phi}}{\sqrt{6} H} , \ \  y_1 = \frac{\sqrt{V_1 e^{-\beta_1 \phi}}}{\sqrt{3} H} , \ \ y_2 = \frac{\sqrt{V_2 e^{-\beta_2 \phi}}}{\sqrt{3} H} ,
\end{equation}
together with
\begin{equation} \label{eq:Densi}
    \Omega_{\rm m} = \frac{\rho_{\rm m}}{3H^2} , \ \ \ \Omega_{\rm r} = \frac{\rho_{\rm r}}{3H^2} \ \ \ \text{and} \ \ \ \Omega_{\phi} = \frac{\rho_{\phi}}{3H^2} \,,
\end{equation}
where $\mbox{m=c+b}$.
Eqs.~\eqref{eq:FriedConst}, \eqref{eq:AccEq} and \eqref{eq:EqMotSF} can then be rearranged into an autonomous system of first-order differential equations:
\begin{align}
    x' &= \frac{1}{\sqrt{6}} f(x,y_1,y_2) - \tilde{h}(x,y_1,y_2) x , \label{eq:SCGDS1} \\
    y_{i}' &= - \sqrt{\frac{3}{2}} \beta_{i} x y_{i} - \tilde{h}(x,y_1,y_2) y_{i} , \label{eq:SCGDS2} \\
    \Omega_{r}' &= - 4 \Omega_r- 2 \tilde{h}(x,y_1,y_2) \Omega_r , \label{eq:SCGDS3}
\end{align}
where a prime denotes a derivative with respect to $\ln a$, $i=1,2$ and we have defined the functions $f \equiv \Ddot{\phi}/H^2$ and $\tilde{h} \equiv \Dot{H}/H^2$. The latter two can be given completely in terms of the variables introduced in eqs.~\eqref{eq:SCGVar} and \eqref{eq:Densi}. Since their expressions are quite long, we refer the reader to Ref.~\cite{Albuquerque:2018ymr} for their explicit forms.  Finally, the Friedmann constraint given by eq.~\eqref{eq:FriedConst} becomes
\begin{equation} \label{eq:SCGFriedConst}
    \Omega_{\rm m}+ \Omega_{\rm r} + \Omega_{\phi} = 1  ,
\end{equation}
where the scalar field density parameter $\Omega_{\phi}$ reads
\begin{equation} \label{eq:SCGOmegaPhi}
    \Omega_{\phi} = x^2 + y_1^2 + y_2^2 + 2 x A \left( \sqrt{6} - \lambda x \right) .
\end{equation}

As such, the SCG model is left with a set of four extra free parameters with respect to $\Lambda$CDM: $\{ A, \beta_1, \beta_2 , \lambda \}$. The range of possible values for these parameters is constrained by the enforcement of theoretical viability conditions for the evolution of both the background and the perturbation sector, including, for example, the conditions for the absence of ghost ($Q_s>0$) and gradient ($c_s^2>0$)  instabilities, which respectively read \cite{Albuquerque:2018ymr}:
\begin{eqnarray}
Q_s&=&\frac{3 x^2 \left(1-2 A \lambda+6 A^2 \right)}
{\left(1-\sqrt{6} A x\right)^2} \,,  \\
c_s^2&=&\frac{3x(1-2A\lambda-2A^2)+4 \sqrt{6} A}
{3x \left( 1-2 A \lambda+6 A^2\right)}  \,.
\end{eqnarray}

We can note that in the limit $A\rightarrow 0$ the above conditions are fully satisfied because the model reduces to  standard Quintessence; if $A\neq0$ these translate into theoretical bounds on $A$ and $\lambda$. A full discussion of their impact on the parameter space can be found in Ref.~\cite{Albuquerque:2018ymr}.

Under the validity of the above conditions, the SCG model has very interesting features: it is possible to realize scaling solutions followed by the dark energy attractor, in this case since the scaling fixed point is stable a second potential is necessary to exit this regime and to start the late-time accelerated expansion; during the early phase of the Universe the scalar field density arising form the cubic $g_3$ term dominates over the standard $g_2$ term while the opposite happens at late-time;  having $A\neq 0$ allows for a wider parameter space for $\beta_1$ and $\beta_2$ compared to a standard Quintessence model, in particular it allows for $\beta_2^2>2$; the scalar field equation of state today, $w_\phi\equiv p_\phi/\rho_\phi$, can be closer to $-1$ than in standard Quintessence.

Finally let us stress that in order to solve the system it is still necessary to provide a set of initial conditions (ICs). In particular, since the model is characterized by a scaling fixed point we can use such scaling solution at early-time to fix the ICs through the model parameters. The ICs for $x_i$ and $y_{1,i}$ are then selected to correspond to the radiation scaling critical point, given by \cite{Albuquerque:2018ymr}
\begin{equation}
    \left( x_i, y_{1,i} \right) = \left( \frac{2 \sqrt{6}}{3 \beta_1} , \frac{\sqrt{12 + 6 A ( 3 \beta_1 - 4 \lambda) }}{3 \beta_1} \right) ,
\end{equation}
while the IC for $y_{2,i}$ is then determined by iteratively solving the background equations until the Friedmann constraint \eqref{eq:SCGFriedConst} is satisfied at present time.

\subsection{Linear Perturbations} \label{sec:IIB}

Let us also consider the perturbed FLRW line element in Newtonian gauge given by
\begin{equation}
    ds^2 = - \left( 1 + 2 \Psi \right) dt^2 + a^2(t) \left( 1 - 2 \Phi  \right) \delta_{ij} dx^i dx^j ,
\end{equation}
where $\Psi(t,x_i)$ and $\Phi(t,x_i)$ correspond to the gravitational potentials and obey the Poisson and lensing equations, given  in Fourier space as follows \cite{Bean:2010zq,Silvestri:2013ne,Pogosian:2010tj}
\begin{align}
    - \frac{k^2}{a^2} \Psi &= 4 \pi G_N \mu (t, k) \rho \Delta , \label{eq:Poisson} \\
    - \frac{k^2}{a^2} \left( \Phi + \Psi \right) &= 8 \pi G_N \Sigma (t, k) \rho \Delta ,
\end{align}
where $k$ is the comoving wavenumber and the comoving density contrast is defined as $\Delta_i \equiv \delta_i + 3H v_i/k $ with $\delta_i = \delta \rho_i / \rho_i $ the density contrast, $\rho_i(t)$ the background energy density of a matter component $i$ and $v_i$ the irrotational component of the peculiar velocity. The two phenomenological functions $\mu$ and $\Sigma$  are, respectively, the effective gravitational coupling, defining the deviation with respect to $\Lambda$CDM on the clustering of
matter and the light deflection parameter characterizing the modifications introduced in the paths travelled by photons on cosmological scales via the modification of the lensing potential $\Phi + \Psi$. Lastly, the difference between the gravitational potentials can be described by the gravitational slip parameter $\eta= \Phi/\Psi$. The $\Lambda$CDM limit is obtained for $\mu = \Sigma = \eta = 1$. As such, any departure from unity translates a signature of modified gravity.

One can obtain approximate analytical expressions for $\mu$, $\Sigma$ and $\eta$ by assuming the quasi-static approximation (QSA)\cite{Boisseau:2000pr,DeFelice:2011hq}, which, in the case of Galileon theory, has been proven to be a valid assumption for modes with $k \gtrsim 0.001 $ h/Mpc \cite{Pogosian:2016pwr,Frusciante:2019xia}. In the specific case of the SCG model, the QSA yields \cite{Albuquerque:2018ymr}
\begin{equation} \label{eq:SCGMu}
\mu = \Sigma = 1 + \frac{6 A^2 x^2 }{Q_sc_s^2(1- \sqrt{6} A x)^2}\,,  \quad \eta = 1.
\end{equation}
Therefore the presence of the cubic coupling  introduces modifications on both the growth of structures $( \mu \neq 1 )$ and the evolution of the weak lensing potential $( \Sigma \neq 1 )$ for all $A \neq 0$. Additionally,  $\mu = \Sigma > 1$ for all viable values of the parameters. As a consequence, we expect the gravitational interaction to be stronger than the one of $\Lambda$CDM.

\begin{table}[t!]
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
Model & $\beta_1$ & $\beta_2$ & $A$ & $ \lambda$ &
$w_{\phi}^{(0)}$\\
\hline\hline
M1  & 100 & 0.7 & -0.3 & 154  & -0.993 \\ \hline
M2  & 100 & 0.7 & 0.09 & -8   &  -0.988 \\ \hline
M3  & 100 & 0.7 &-0.28 & 148.3& -0.993 \\ \hline
M4  & 100 & 2.5 & -1   &  150 & -0.975 \\   \hline
\end{tabular}
\end{center}
\caption{\label{tab:Models}
Model parameters $\{ \beta_1 , \beta_2 , A , \lambda \}$ for the four case-study SCG models. In addition to the parameter values, we also show today's dark energy equation
of state $w_{\phi}^{(0)}$.}
\end{table}

Let us stress that while here we present the equations under the QSA, in what follows we shall not rely on this approximation and instead evolve the full linear perturbation equations. The discussion in this section will, nevertheless, help in the interpretation of the results we present in Sec.~\ref{sec:CosmPert}.

\section{Cosmological Observables}\label{Sec:CosmoObs}

\subsection{Methodology} \label{Sec:Method}

The main goal of this project is to investigate the evolution of linear cosmological perturbations and obtain observational constraints on the SCG model. To achieve this, we make use of the Effective Field Theory (EFT) formalism \cite{Gubitosi:2012hu,Bloomfield:2012ff}  (see Ref.~\cite{Frusciante:2019xia} for a review) and then resort to the public available Einstein-Boltzmann code \texttt{EFTCAMB} \cite{Hu:2013twa}\footnote{Web page: \url{http://www.eftcamb.org}} and MCMC engine \texttt{EFTCosmoMC} \cite{Raveri:2014cka}. As such, in this section we briefly discuss the implementation of the SCG model in \texttt{EFTCAMB}.

The EFT offers a model-independent framework to describe both the background evolution of the Universe and the behaviour of linear cosmological perturbations in gravity theories with a single additional scalar DoF. This description is made in terms of a set of free functions of time known as EFT functions. The EFT action encompassing Galileon theory with the additional consideration of the bound on the speed of propagation of tensor modes coming from GWs ($c_T^2=1$) is
\begin{align}
    \mathcal{S} = &\int d^4 x \sqrt{-g} \frac{m_0^2}{2} \Bigg\{ \left( 1 + \Omega (t) \right) + \frac{2 \Lambda (t)}{m_0^2} - \frac{2 c(t)}{m_0^2} \delta g^{00} \nonumber \\
    &+ H_0^2 \gamma_1 (t) \left( \delta g^{00} \right)^2 - H_0 \gamma_2 (t) \delta g^{00} \delta K \Bigg\} + \mathcal{S}_{\gamma} \ , \label{eq:EFTAction}
\end{align}
where $m_0^2$ is the Planck mass and $\delta g^{00}$ and $\delta K$ are the linear perturbations of the upper time-time metric component and the trace of the extrinsic curvature $K^{\mu}_{\nu}$, respectively. The time dependent prefactors  $\{ \Omega, \Lambda, c, \gamma_1, \gamma_2 \}$ are the aforementioned  EFT functions.

The action \eqref{eq:EFTAction} can then be connected to a specific Galileon model by finding the corresponding forms of the EFT functions through a procedure known as \textit{mapping} \cite{Gleyzes:2013ooa,Bloomfield:2013efa,Frusciante:2016xoj}. For the SCG model, we follow the procedure depicted in Ref.~\cite{Frusciante:2016xoj} and find:
\begin{align}
    \frac{c a^2}{m_0^2} &= 3 \mathcal{H}^2 x^2 + A \mathcal{H}^2 \Big[ 3 \sqrt{6} x - 6 \lambda x^2 - \sqrt{6} b(x)  \Big] , \\
    \frac{\Lambda a^2}{m_0^2} &= 3 \mathcal{H}^2 \left( x^2 - y_1^2 - y_2^2 \right) - 2 \mathcal{H}^2 A \Big[ 3 \lambda x^2 + \sqrt{6} b(x) \Big] , \\
    \gamma_1 &= \sqrt{\frac{3}{4}} \frac{A \mathcal{H}^2}{a^2 H_0^2} \left( b(x) - 3x \right) , \label{eq:SCGG1} \\
    \gamma_2 &= - \frac{2 \sqrt{6} A \mathcal{H}}{a H_0} x , \label{eq:SCGG2}
\end{align}
where  $b(x) = x' + \tilde{h}x$ and $\mathcal{H}$ is the Hubble function in conformal time $\tau$. The use of conformal time and the redefinitions of $c$ and $\Lambda$ are done to match the notation of the \texttt{EFTCAMB} code. Let us note that $\Omega = 0$ in the SCG.

From the forms of $\gamma_1$ and $\gamma_2$, the two EFT functions which impact the linear perturbation sector only, we can expect modifications in the growth of perturbations to arise when the parameter $A$, present in both \eqref{eq:SCGG1} and \eqref{eq:SCGG2}, is non-zero. On the other hand, the $\lambda$ parameter, which appears on the background EFT functions $c$ and $\Lambda$, will consequently propagate its effect through the background evolution.

Finally,
we have implemented the previous EFT functions together with a background solver, composed by eqs.~\eqref{eq:SCGDS1}-\eqref{eq:SCGDS2}, in \texttt{EFTCAMB}, with the purpose of obtaining theoretical predictions for  cosmological observables and observational constraints on the SCG parameters using \texttt{EFTCosmoMC}. We stress that \texttt{EFTCAMB} solves the full linear perturbation equations without resorting to the QSA approximation.

\begin{figure}[t!]
\centering
\includegraphics[scale=0.40]{Figures/Psi_MModels_in_z_OV.pdf}
\caption[Evolution of $\Psi$ as a function of redshift for the M models]{(Top) Evolution of the metric potential $\Psi$ normalized by its initial value $\Psi_i$ as a function of redshift $z+1$ for the wavenumber $k = 0.01$ Mpc$^{-1}$. The evolution of $\Psi/\Psi_i$ is shown for the four models of Table \ref{tab:Models}, specifically: M1 (dashed blue line), M2 (dot-dashed magenta line), M3 (dotted red line) and M4 (long dashed green line), as well as for $\Lambda$CDM (solid black line). (Bottom) Percentage relative difference of the models' $\Psi$ with respect to $\Lambda$CDM.  \label{fig:SCGPhi}}
\end{figure}
\subsection{Phenomenology} \label{sec:CosmPert}

In this section we study the dynamics of scalar cosmological perturbations in the SCG model and analyse their impact on some cosmological observables. For our investigation, we consider four Models (M) specified by the parameters listed in Table \ref{tab:Models}. The choice of these values is purely illustrative, nevertheless they satisfy the stability requirements previously discussed. Notably we have verified that the $\beta_1$ and $\beta_2$ parameters do not have any direct impact on the phenomenology of the SCG we are going to present. Even so, they indirectly impact the parameter space, e.g.\ larger values of $\beta_2$ allow to explore regions of the parameter space with larger values of $A$ (see Ref.~\cite{Albuquerque:2018ymr}). The cosmological parameters are fixed to be: $H_0=70$ km/s/Mpc, the baryon and cold dark matter energy densities are $\Omega_{\rm b}h^2= 0.0226$ and $\Omega_{\rm c}h^2= 0.112$, where $h=H_0/100$, and finally the amplitude and tilt of the primordial power spectrum are $A_{\rm s}= 2.1 \times 10^{-9}$ and $n_s=0.96$. Let us stress that the cosmological parameters are kept fixed only for the purpose of the phenomenological analysis, as in this case we are able to trace back to the impact of MG on cosmological observables when compared to $\Lambda$CDM. We divide our discussion considering the three main effects we identify, i.e.\ on the gravitational lensing potential and its time derivative (ISW effect) and on the evolution of matter density perturbations.

\subsubsection{Impact on gravitational lensing} \label{Sec:GravLen}

The lensing potential $\phi_{\rm len} = \left( \Phi + \Psi \right)/2$ for the SCG model is modified compared to $\Lambda$CDM. In Figure \ref{fig:SCGPhi} we show the evolution of the gravitational potential $\Psi$ normalized by its initial value as a function of the scale factor for a fixed $k=0.01$ Mpc$^{-1}$. Let us recall that in this model $\Phi=\Psi$, therefore $\phi_{\rm len}=\Psi$.
We note that at late-time the gravitational potential for M1, M3 and M4 is enhanced with respect to $\Lambda$CDM, on the contrary for M2  it is suppressed. The largest deviation occurs for M4 ($\sim 26 \%$ at present time, $z\sim 0$), the model with the largest value of $A^2$, as expected from eq.~\eqref{eq:SCGMu}.
Following this line of thinking, we would expect the growing order in deviation from $\Lambda$CDM to be M2 $<$ M3 $<$ M1 $<$ M4, considering the values of $A$ presented in Table \ref{tab:Models}. However, this is not the case: M3 is slightly above M1. This is due to the $\lambda$ parameter, whose value is noticeably smaller for M3 than M1, which enters in the $Q_sc_s^2$ term in eq.~\eqref{eq:SCGMu}. This makes $\mu(M3)>\mu(M_1)$ for $z+1<10^3$. Furthermore, the gravitational potential of M2 is suppressed with respect to $\Lambda$CDM, contrary to the small enhancement expected from eq.~\eqref{eq:SCGMu}. This is due to a suppression of the matter density perturbation with respect to the standard model. We further discuss this feature in Sec.~\ref{Sec:MatterPS}. These modifications in the lensing potential are mirrored in the lensing angular power spectra as shown in Figure \ref{fig:SCGLenPS}. Finally,  M4 is the only case which generates a significant large deviation from $\Lambda$CDM at early time as confirmed  by  the evolution of $\Psi$. The latter is connected to the evolution of $y_1$ which is the dominant component at early-time (see Figure \ref{fig:SCGy1}). Models that show early-time modifications of gravity \citep{Lin:2018nxe,Benevento:2018xcu} are known to alter the amplitude and phase of the high-$\ell$ acoustic peaks of the CMB temperature-temperature (TT) power spectrum. This is indeed what we find in Figure \ref{fig:SCGCMBTTPS} for M4.

\begin{figure}[t!]
\centering
\includegraphics[scale=0.40]{Figures/LenPS_MModels_OV.pdf}
\caption[ISW source for the M models]{(Top) Lensing angular power spectra $D_{\ell}^{\phi \phi} = \ell (\ell + 1) C_{\ell}^{\phi \phi}/(2\pi)$ for $\Lambda$CDM (solid black line) and the four M models of Table \ref{tab:Models}, namely: M1 (dashed blue line), M2 (dot-dashed magenta line), M3 (dotted red line) and M4 (long dashed green line). (Bottom) Difference between the lensing power spectra of each of the M models and that of $\Lambda$CDM. \label{fig:SCGLenPS}}
\end{figure}

\begin{figure}[t!]
\centering
\includegraphics[scale=0.40]{Figures/y1_MModels_OV.pdf}
\caption[Evolution of y1]{Evolution of the $y_1$ variable for the models M1 (dashed blue line), M2 (dot-dashed magenta line), M3 (dotted red line) and M4 (long dashed green line).  \label{fig:SCGy1}}
\end{figure}

\begin{figure*}[t!]
\centering
\includegraphics[scale=0.35]{Figures/TTPS_MModels_OV.pdf}
\caption[CMB TT power spectra for the M models]{(Top) CMB temperature-temperature (TT) angular power spectra $D_{\ell}^{TT} = \ell (\ell + 1) C_{\ell}^{TT}/(2\pi) $ for $\Lambda$CDM (solid black line) and the four M models of Table \ref{tab:Models}, namely: M1 (dashed blue line), M2 (dot-dashed magenta line), M3 (dotted red line) and M4 (long dashed green line). On the top-right corner is shown a zoom at large angular scales (small $\ell$) of this same quantity. (Bottom) Percentage relative difference between the lensing power spectra of each of the M models and that of the M models' TT power spectra with respect to $\Lambda$CDM. \label{fig:SCGCMBTTPS}}
\end{figure*}

\subsubsection{Impact on the Integrated Sachs-Wolfe (ISW) effect}

A difference in the evolution of the gravitational potentials relative to the standard cosmological model impacts the ISW effect which is sourced by the time derivative of $\Psi + \Phi$. We show the evolution with redshift of $\dot{\Psi}+\dot{\Phi}$ for a fixed $k=0.01$ Mpc$^{-1}$ in Figure \ref{fig:SCGISWSour}. In the latter, M1, M2 and M3 closely follow the behaviour of $\Lambda$CDM for almost all $z$, showing some larger deviations at intermediate redshift ($10<z<100$). Then, while models M1 and M3 become slightly enhanced at present time, with the enhancements being of about $\sim 0.3\%$ and $\sim 2\%$ respectively, M2 is suppressed by $\sim 5\%$. M4 is the model which shows the larger deviations from $\Lambda$CDM at all redshift. Despite being suppressed with respect to the standard model for most of its evolution, it then becomes enhanced at late-time, reaching a $\sim 12\%$ enhancement relative to $\Lambda$CDM at present time.

\begin{figure*}[t!]
\centering
\includegraphics[scale=0.35]{Figures/ISWS_MModels_OV.pdf}
\caption[Evolution of the ISW source for the M models]{(Top) Evolution of the time derivative of $\Psi + \Phi$, computed at $k = 0.01$ Mpc$^{-1}$, for $\Lambda$CDM (solid black line) and the four M models of Table \ref{tab:Models}, namely: M1 (dashed blue line), M2 (dot-dashed magenta line), M3 (dotted red line) and M4 (long dashed green line). It is accompanied by a zoom at late-time of the same quantity. (Bottom) Percentage relative difference of the M models' $\Dot{\Psi} + \Dot{\Phi}$ computed with respect to $\Lambda$CDM.  \label{fig:SCGISWSour}}
\end{figure*}
The change in the ISW effect affects the CMB TT angular power spectrum through the radiation transfer function \cite{Seljak:1996is}. We show the TT power spectra for the SCG and $\Lambda$CDM in Figure \ref{fig:SCGCMBTTPS}. Firstly, modifications in the time evolution of the gravitational potentials at late-time induce a late-time ISW effect which alters the low-$\ell$ tail. For the SCG,  M1, M3 and M4 show a suppressed ISW tail with respect to $\Lambda$CDM while M2 is slightly enhanced. Secondly, changes in $\dot{\Phi}+\dot{\Psi}$ during the transition from the radiation era to the matter one generate an early-time ISW effect that alters the amplitude of the first acoustic peak. Indeed we notice that M4's has a smaller amplitude. It has been found that models with a suppressed ISW tail are statistically favored by CMB data \cite{Frusciante:2019puu,Peirone:2019aua,Atayde:2021pgb}. On the contrary those with a large deviation in the late-time ISW source are ruled out \cite{Renk:2017rzu,Peirone:2017vcq}.

\begin{figure}[t!]
\centering
\includegraphics[scale=0.40]{Figures/MatPS_MModels_OV.pdf}
\caption[Matter Power Spectra for the M models]{(Top) Matter power spectra $P(k)$ for $\Lambda$CDM (solid black line) and the four M models of Table \ref{tab:Models}, specifically: M1 (dashed blue line), M2 (dot-dashed magenta line), M3 (dotted red line) and M4 (long dashed green line). (Bottom) Percentage relative difference of the matter power spectra computed with respect to $\Lambda$CDM. \label{fig:SCGMattPS}}
\end{figure}

\subsubsection{Impact on the growth of matter perturbations and the distribution of large-scale structures} \label{Sec:MatterPS}

The power spectrum of matter density fluctuations $P(k)$ for the SCG model shows deviations with respect to $\Lambda$CDM for $k > 10^{-3} \ h$Mpc$^{-1}$, as depicted in Figure \ref{fig:SCGMattPS}. We find it to be enhanced for models M1, M3 and M4 whereas M2 becomes suppressed. The enhancements are in agreement with the observed behaviour of $\mu$, with the largest deviation (up to $66 \%$ for larger $k$), being for the case with the largest value of $A^2$: M4.
\begin{figure}[t!]
\centering
\includegraphics[scale=0.4]{Figures/Hdiff_MModels_in_z_OV.pdf}
\caption[Difference in the Hubble rate]{Evolution of the relative difference of the Hubble parameter $H(t)$ for the M models featured in Table \ref{tab:Models} with respect to $\Lambda$CDM. Model M1 is presented in a dashed blue line, M2 in a dot-dashed magenta line, M3 in a dotted red line and M4 in a long dashed green line. \label{fig:SCGHDiff}}
\end{figure}
The suppression of M2 can be explained by considering that this case has the largest deviation in $H(t)$ relative to $\Lambda$CDM as shown in Figure \ref{fig:SCGHDiff}. This affects the evolution of the matter density perturbations because it enters as a friction term in the equation $\Ddot{\delta} + 2 H \Dot{\delta} -4 \pi G_N \mu (t) \rho \delta = 0$, hindering the growth of matter perturbations. The modifications introduced by $\mu$ are negligible for M2 because $\mu \sim 1$ at all times.
The described effect has previously been observed for standard Quintessence \cite{Alimi:2009zk}.

\section{Observational Constraints} \label{Sec:Constraints}

Now that we have investigated the phenomenology of the SCG, we want to test the theoretical predictions with observations. In order to do this, we make use of \texttt{EFTCosmoMC} \cite{Raveri:2014cka}, a modification of the public \texttt{CosmoMC} software \cite{Lewis:2002ah,Lewis:2013hha}, that allows to sample the free parameter space using a  MCMC method, compute theoretical predictions through our modified version of \texttt{EFTCAMB} and compare them with observational data, thus reconstructing the posterior distribution of the sampled parameters.

As our baseline dataset we use here the {\it Planck} 2018 \cite{Planck:2019nip} (hereafter ''Planck'') data of CMB temperature likelihood for large angular scales $\ell =[2,29]$ and for the small angular scales a joint of TT, TE and EE likelihoods ($\ell =[30,2508]$ for TT power spectrum, $\ell =[30,1996]$ for TE cross-correlation and EE power spectra).
 We also explore the effect on the constraints obtained adding other datasets to our baseline: we consider the combination Planck+lensing, where we also include the CMB lensing potential data from {\it Planck} ~\cite{Planck:2019nip,Planck:2018lbu}, and the combination Planck+BAO+SN where we also include baryon acoustic oscillations (BAO) data from the 6dF Galaxy Survey \cite{Beutler:2011hx}, the Sloan Digital Sky Survey (SDSS) DR7 Main Galaxy Sample \cite{Ross:2014qpa} and SDSS DR12 consensus release \cite{BOSS:2016wmc}, and supernova (SN) data from Pantheon \cite{Pan-STARRS1:2017jku}.

For all these combinations, our set of free parameters includes the standard cosmological parameters, i.e.\ the baryon and cold dark matter energy densities $\Omega_{\rm b}h^2$ and $\Omega_{\rm c}h^2$, the amplitude and tilt of the primordial power spectrum $A_{\rm s}$ and $n_s$, the optical depth $\tau$ and the angular size of the sound horizon at recombination $\theta_s$.  In addition to these, we also consider as free the SCG parameters $A$ and $\lambda$ and  we sample them in the range $A\in [0,3]$ and $\lambda \in [-100,0]$. Notice that here we consider the parameters $\beta_1$ and $\beta_2$ as fixed, given that, as it is discussed in Sec.~\ref{sec:CosmPert}, they have a negligible or no-impact on the observables under consideration.  We set them to the values $\beta_1=100$ and $\beta_2=0.7$. We nevertheless verified, in our baseline data case, that including them in the analysis and marginalising them out does not affect the final results. We use flat priors on all the sampled parameters.  Finally, we impose the stability conditions to avoid ghost and gradient instabilities \cite{DeFelice:2016ucp,Frusciante:2018vht} which are directly computed by \texttt{EFTCAMB} thanks to a stability built-in module, thus rejecting all sampled points in the parameter space that do not satisfy these conditions.

Once we obtain the sampled chains from \texttt{EFTCosmoMC} we analyze them using \texttt{GetDist} \cite{Lewis:2019xzd}.

\subsection{Results}

We show in \autoref{fig:baseline} and \autoref{tab:baseline} the results obtained in our baseline case, i.e.\ when only Planck data are considered, on the primary sampled parameters $\tau$, $n_s$, $A$ and $\lambda$, and on the derived parameters $H_0$, $\Omega^0_{\rm m}$ and $S^0_8=\sigma_8\sqrt{\Omega^0_{\rm m}/0.3}$, with $\sigma_8$ the dispersion of density perturbations on a scale of $8$ $h^{-1}$ Mpc.

We notice that the SCG parameter $A$, which can be considered as an amplitude of the deviation from GR, is constrained to be very small, thus highlighting the preference of Planck data for a GR cosmology. The parameter $\lambda$ is instead poorly constrained, mainly due to the fact that its effects become negligible as $A$ gets close to zero.

Concerning the standard cosmological parameters, we notice that allowing for a SCG cosmology has the effect of shifting the constraints on $H_0$ towards smaller values with respect to the $\Lambda$CDM case, while $\Omega^0_{\rm m}$ takes slightly larger values and the other parameters are mostly unchanged. The first of these effects however is significant; the Planck data give a value for $H_0$ in $\Lambda$CDM that is in tension of approximately $4.5\sigma$ with local measures (see e.g.\ \cite{DiValentino:2020zio} for an extensive review), which prefer higher values of this parameter. While one hopes that new physics would be able to reconcile this tension, we notice that the SCG does not allow to ease the difference between low and high redshift observables, as it instead increases it even if not in a significant way. In Quintessence models it has been found that having $w_{\phi} > -1$ worsens the $H_0$ tension \cite{Banerjee:2020xcn}. For our model, if we consider the mean values obtained with the Planck dataset we find $w_{\phi,0} = - 0.98$. As for Quintessence, this might be one of the reasons why the SCG is incapable of solving the $H_0$ tension.

In addition to this, we notice that the minimum $\chi^2$ ($\chi^2_{\rm min}$) increases when one fits the Planck data in the SCG model with respect to the $\Lambda$CDM model. This appears to be counter intuitive, as the former model has two additional parameters with respect to the latter; however, the SCG model we investigate does not have a $\Lambda$CDM limit, but rather reduces to Quintessence when $A=0$, a limit that anyway lies at the very edge of the prior range. For such reason, we can interpret this increase in $\chi^2_{\rm min}$ as an hint that $\Lambda$CDM is still the model favoured by the data, with even the Quintessence $A=0$ limit of SCG having a worse goodness of fit with respect to it.

\begin{figure}[t!]
	\centering
	\includegraphics[width=1.\columnwidth]{Figures/comparison_Planck.pdf}
	\caption{$68\%$ and $95\%$ confidence level contours obtained using the Planck dataset for the SCG model (red) and for a $\Lambda$CDM cosmology. }\label{fig:baseline}
\end{figure}

\begin{table}[t!]
    \centering
    \begin{tabular}{c|c|c}
Parameter          &  SCG                          & $\Lambda$CDM\\
\hline
$\tau$             & $0.0548^{+0.0068}_{-0.0080}$ & $0.0540\pm 0.0078$\\
$H_0$              & $66.94\pm 0.61$              & $67.88\pm 0.62$\\
$\Omega^0_{\rm m}$ & $0.3189\pm 0.0083$           & $0.3091\pm 0.0083$\\
$S^0_8$            & $0.839\pm 0.016$             & $0.837\pm 0.016$\\
$n_s$              & $0.9632\pm 0.0044$           & $0.9653\pm 0.0044$\\
$A$                & $< 0.0133$                   & ...\\
$\lambda$          & $> -56.0$                    & ...\\
\hline
$\chi^2_{\rm min}$ & $2774$                       & $2771$
    \end{tabular}
    \caption{$68\%$ limits on the cosmological and SCG parameters obtained using Planck data for a SCG and a $\Lambda$CDM cosmology and their  minimum $\chi^2$ ($\chi^2_{\rm min}$).}
    \label{tab:baseline}
\end{table}

In \autoref{fig:allobs} and \autoref{tab:allobs} we compare instead our baseline results on the SCG model with those obtained when using the data combinations Planck+lensing and Planck+BAO+SN.
We notice that the inclusion of additional dataset does not improve significantly the constraints on the SCG parameters, with the exception of Planck+BAO+SN that seems to exhibit a peak for $\lambda$ for a non-vanishing value. However, despite a good convergence of the chains, this effect might be due to the aforementioned degeneracies between $\lambda$ and $A$ with the former that is allowed to take any value when the latter vanishes, a degeneracy that might not allow a good sampling with the Metropolis-Hastings algorithm employed by EFTCosmoMC.

The bounds on the cosmological parameters are instead tightened by the inclusion of the additional datasets, with the important features of $H_0$ being brought back to the Planck value for $\Lambda$CDM when we consider Planck+BAO+SN. In this case, the data still allow for a departure from GR, encoded in the non-vanishing value of $A$, avoiding the worsening of the tension with low redshift data that we noticed in the Planck case.

\begin{figure}[!h]
	\centering
	\includegraphics[width=1.\columnwidth]{Figures/allobs_SCG.pdf}
	\caption{$68\%$ and $95\%$ confidence level contours obtained in a SCG cosmology for the Planck data (red), the Planck+lensing combination (yellow) and Planck+BAO+SN (purple).\label{fig:allobs}}
\end{figure}

\phantom{text needed to not mess up the layout}

\begin{table}[!h]
    \centering
    \begin{tabular}{c|c|c|c}
Parameter          &  Planck                      & Planck+lensing     & Planck+BAO+SN\\
\hline
$\tau$             & $0.0548^{+0.0068}_{-0.0080}$ & $0.0541\pm 0.0074$ & $0.0556\pm 0.0079$\\
$H_0$              & $66.94\pm 0.61$              & $67.08\pm 0.54$    & $67.46\pm 0.47$\\
$\Omega^0_{\rm m}$ & $0.3189\pm 0.0083$           & $0.3168\pm 0.0072$ & $0.3116\pm 0.0059$\\
$S^0_8$            & $0.839\pm 0.016$             & $0.834\pm 0.013$   & $0.826\pm 0.012$\\
$n_s$              & $0.9632\pm 0.0044$           & $0.9637\pm 0.0042$ & $0.9659\pm 0.0039$\\
$A$                & $< 0.0133$                   & $< 0.0126$         & $< 0.0129$\\
$\lambda$          & $> -56.0$                    & $> -55.9$          & $49^{+36}_{-27}$\\
    \end{tabular}
    \caption{$68\%$ limits on the cosmological and SCG parameters obtained in a SCG cosmology for the dataset combinations Planck, Planck+lensing and Planck+BAO+SN.}
    \label{tab:allobs}
\end{table}

\section{Conclusion}\label{Sec:Conclusion}

We studied for the first time the phenomenology at large linear scales of a Scaling Cubic Galileon model given by the Lagrangian \eqref{eq:SCGaction} and characterized by four additional parameters $\{A,\lambda, \beta_1, \beta_1\}$ in comparison to the standard cosmological model. Furthermore, we provided the cosmological constraints using CMB, CMB lensing, BAO and SN data.

The model shows very interesting features. Firstly, the early time scaling regime after which solutions approach a late time attractor offers the model the opportunity to be compatible with particle physics' energy scale at early-time while still realizing late-time cosmic acceleration. Regarding the evolution of linear cosmological perturbations, the modifications of the gravitational potentials are identified to be weighed largely by the parameter $A$ even though $\lambda$ can also have a relevant impact.
The remaining two parameters, $\beta_1$ and $\beta_2$, have no direct impact on the perturbations but they change the parameter space of $A$.
We identify three main effects on the cosmological observables: deviations in the lensing potential, which can be either suppressed or enhanced with respect to the $\Lambda$CDM model and correspondingly leads to a suppressed/enhanced lensing angular power spectrum. Additionally, the changes in the lensing potential also modify the high-$\ell$ acoustic peaks of the temperature-temperature power spectrum. Following this, a change in the time derivative of the gravitational potentials is then expected which modifies the ISW effect. Indeed we found that modifications in the early ISW effect led to a lower amplitude of the first acoustic peak of the temperature-temperature power spectrum for the SCG model. The latter is also modified in the low-$\ell$ tail where in this case the differences with respect to $\Lambda$CDM were due to modifications in the late ISW effect. Finally, the power  spectrum  of  matter  density  fluctuations is also enhanced/suppressed with respect to the standard scenario. The modifications are driven mostly by $A^2$ which enhances the matter power spectrum. We found that there are cases for which  modifications in the background expansion give rise to a friction term that dominates over any other modified gravity source, leading to a suppressed matter power spectrum.

We tested these effects with cosmological data and we found that the SCG model is also suffering from the $H_0$ tension when using only Planck CMB data which is even worse than the $\Lambda$CDM model. The joint analysis of CMB, BAO and SN data was able to set an upper bound on the parameter $A<0.0129$ and to constrain $\lambda=49^{+36}_{-27}$ at 68\% C.L.. The parameter $A$ is then very close to zero which in turn led to loose power in constraining on $\lambda$. Furthermore, the SCG model exasperates the $H_0$ tension between Planck data and local measurements.

In conclusion if on one side the SCG model eases some issues of the $\Lambda$CDM model, on the other side the $H_0$ tension is still present. It would then be of interest to consider the model for further investigations in the future, particularly once new data are available, which will also help in shedding light on the nature of this tension.

\begin{acknowledgements}
We thank N.~J.~Nunes for useful discussion.
ISA and NF acknowledge support by Funda\c{c}\~{a}o para a  Ci\^{e}ncia e a Tecnologia (FCT) through the research grants UIDB/04434/2020, UIDP/04434/2020, PTDC/FIS-OUT/29048/2017, CERN/FIS-PAR/0037/2019, PTDC/FIS-AST/0054/2021. The research of ISA has received funding from the FCT PhD fellowship grant with ref.~number 2020.07237.BD. NF  acknowledges support from her FCT research grant ``CosmoTests -- Cosmological tests of gravity theories beyond General Relativity" with ref.~number CEECIND/00017/2018.
MM acknowledges support from ``la Caixa'' Foundation (ID 100010434), with fellowship code LCF/BQ/PI19/11690015, and the Centro de Excelencia Severo Ochoa Program SEV-2016-059.
\end{acknowledgements}

\normalem

redpajama_set_name: RedPajamaArXiv


text:
Troy Smith (* 11. April 1987) ist ein jamaikanischer ehemaliger Fußballspieler auf der Position eines Mittelfeld- und Flügelspielers, der auf in der Defensive zum Einsatz kam.

Im Alter von etwa 28 Jahren musste der jamaikanische Nationalspieler aufgrund einer schweren Knieverletzung seine Karriere beenden.

Vereinskarriere

Karrierebeginn und Zeit bei Village United
Troy Smith wurde am 11. April 1987 geboren und spielte bereits während seiner Schulzeit, die er mitunter an der 1973 gegründeten Bounty Hall Primary and Infant School, kurz BHPIS, im Landesinneren hinter Falmouth und Martha Brae gelegen, verbrachte, Fußball. Im Jahre 2005 wurde der 18-Jährige in die Herrenmannschaft des Village United FC, einem Fußballverein aus Falmouth, aufgenommen. In der Saison 2005/06 konnte Smith in weiterer Folge seinen ersten Treffer in der höchsten jamaikanischen Fußballliga verzeichnen und beendete die Spielzeit mit der Mannschaft im Endklassement auf dem sechsten Rang. Während die Mannschaft 2005/06 im jamaikanischen Fußballpokal im Achtelfinale ausschied, gewann das Team den regionalen Trelawny Cup gegen die Fußballauswahl von Clark's Town, wobei sich jedoch der unterlegene Finalist für den ein Jahr später stattfindenden jamaikanischen Cup qualifizierte, da Village United als Erstligist automatisch für den Pokal teilnahmeberechtigt ist.

Auch in der darauffolgenden Spielzeit kam die Mannschaft nicht über einen Platz im Tabellenmittelfeld und das Viertelfinale im jamaikanischen Fußballpokal hinaus. In der Saison 2006/07 stand Smith mit Village United abermals im Finale des Trelawny Cups. 2007/08 musste Smith, der es auf insgesamt acht Tore – davon fünf vom Elfmeterpunkt – gebracht hatte, mit seinem Team sogar in die Relegation, wobei die Mannschaft in dieser jedoch noch einen Abstieg abwenden konnte. Positiv zu vermerken ist in dieser Saison Village Uniteds Einzug ins Halbfinale des jamaikanischen Cups, in dem die Mannschaft gegen den späteren Pokalsieger Waterhouse FC mit 2:4 ausschied.

In der Endtabelle der regulären Saison 2008/09 rangierte Smith mit seiner Mannschaft auf einem Abstiegsplatz, konnte mit dem Team jedoch in der nachfolgenden Relegationsgruppenphase doch noch den Klassenerhalt schaffen. Über das Viertelfinale – Village United unterlag Waterhouse klar mit 0:6 – kam der Mittelfeldakteur mit seiner Mannschaft im jamaikanischen Fußballpokal 2008/09 nicht hinaus. 2009/10 trat Smith für die Mannschaft aus Trelawny wieder torgefährlich in Erscheinung. Dabei erzielte er elf der 29 Tore seiner Mannschaft in der regulären Saison, wobei Smith weiterhin die Elfmeter seines Teams übernahm – acht seiner elf Treffer waren vom Elfmeterpunkt. Aufgrund des sechsten Platzes qualifizierte sich das Team für die saisonentscheidende Meisterschaftsgruppe, in der das Team jedoch nur den sechsten belegte. Ebenfalls 2009/10 scheiterte Village United am Viertelfinale des jamaikanischen Fußballpokals.

Zu Beginn der Spielzeit 2010/11 wechselte Village United seine Heimspielstätte und trug seine Partien nicht mehr in Falmouth, sondern fortan in Montego Bay aus. Die gesamte Saison verlief in etwa wie die vorhergegangene. Smith, der über einen längeren Zeitraum als Mannschaftskapitän fungierte, rangierte mit Village United am Ende der regulären Saison auf dem sechsten Tabellenplatz, schaffte dadurch die Qualifikation für die Meisterschaftsgruppenphase und wurde in dieser abermals Sechster. Frühzeitig – in Runde 1 – schied das Team jedoch im jamaikanischen Fußballpokal aus. Bereits im Sommer 2010 erhielt Smith, der davor bereits mehrfach für die Juniorenauswahlen Jamaikas zum Einsatz gekommen war, seine erste Einberufung in die A-Nationalmannschaft seines Heimatlandes und trat fortan regelmäßig für diese in Erscheinung.

Wechsel zu Montego Bay United
Vom mittlerweile in Montego Bay spielenden Village United wechselte Smith während der bereits laufenden Saison 2011/12 innerhalb der Stadt zu Montego Bay United. Die Mannschaft trat bis zu dieser Zeit als Seba United in Erscheinung und hatte in der vergangenen Saison noch in der jamaikanischen Zweitklassigkeit gespielt. Erst nach der Übernahme des Klubs durch Orville Powell wurde der Aufsteiger im Sommer 2011 in Montego Bay United umbenannt. Im Endklassement rangierte der Klub auf dem siebenten Platz und musste in die Relegation. Dort konnte der Klassenerhalt gesichert werden; Smiths ehemaliger Verein jedoch musste den Weg in die Zweitklassigkeit antreten. Der jamaikanische Pokal wurde in dieser Saison nicht ausgetragen.

Ähnlich erging es der Mannschaft in der darauffolgenden Spielzeit 2012/13. Nach einem siebenten Platz am Ende der regulären Saison musste Smith mit Montego Bay United in die Relegation und belegte auch am Ende den siebenten Platz. Weitaus erfolgreicher verlief die nachfolgende Saison, in der es das Team bis auf den dritten Tabellenplatz brachte und in der saisonentscheidenden Meisterrunde Harbour View FC im Halbfinale und danach im Finale den Waterhouse FC mit 5:2 besiegte. Des Weiteren schaffte er es mit dem Team ins Finale um den jamaikanischen Fußballpokal und unterlag mit seiner Mannschaft nur knapp dem Reno FC mit 3:4. Aufgrund des Meistertitels qualifizierte sich Montego Bay United zusammen mit dem zweitplatzierten Waterhouse FC für die CFU Club Championship 2015. Bei dieser Karibik-Klubmeisterschaft konnte sich Smith mit seinem Team als Erster der Gruppe 3 für die abschließende Finalrunde qualifizieren, ehe die Mannschaft im Halbfinale der W Connection aus Trinidad und Tobago unterlag, aber im Spiel um Platz 3 den Don Bosco FC aus Haiti mit 1:0 abfertigte.

Die Quellen belegen jedoch nicht eindeutig, dass Smith in diesem Zeitraum der Mannschaft angehörte. Während er laut transfermarkt.de im Zeitraum von 2012 bis 2015 Spieler von Montego Bay United war, gehen andere Statistikseiten wie nationalfootballteams.com davon aus, dass Smith zwischenzeitlich nicht Teil des jamaikanischen Erstligisten war. Darauf lässt auch ein Artikel aus dem Jamaica Online Star von Anfang des Jahres 2015 schließen. Darin heißt es, dass Smith mit Montego Bay United in Verbindung gebracht werde. Auch ein Artikel im Jamaica Observer von Mitte Februar 2015 lässt darauf schließen, dass Smith sich erst 2015 wieder dem Verein angeschlossen hat. Gesichert ist jedoch, dass er in der Saison 2014/15 für den Klub aus Montego Bay in Erscheinung getreten ist, im Endklassement den zweiten Platz belegte (nach einer 0:2-Niederlage im Finalspiel gegen Arnett Gardens) und danach seine Karriere als Profifußballspieler aufgrund einer schweren Knieverletzung im Alter von etwa 28 Jahren beendete.

Danach versuchte sich der in Bounty Hall ansässige Smith für einige Zeit als Spieler des unterklassigen Harmony FC, bei dem er als Offensivspieler und bester Torschütze der Mannschaft fungierte. Im Jahre 2017 noch äußerst torgefährlich, scheint er nur mehr kurz in den Spielberichten des Jahres 2018 auf, ehe er wieder beschäftigungslos wurde. In einem Zeitungsartikel im Jamaica Star berichtete Smith im Juni 2019 zurzeit ohne Beschäftigung zu sein und bereits seit Jahren des Öfteren die Schüler an seiner Alma Mater zu trainieren.

Nationalmannschaftskarriere
Bevor Smith in der A-Nationalmannschaft seines Heimatlandes spielte, trat er bereits für jamaikanische U-20- und U-23-Auswahl in Erscheinung. Für ein Freundschaftsspiel gegen Trinidad und Tobago holte ihn Nationaltrainer Theodore Whitmore im August 2010 erstmals in die A-Nationalmannschaft Jamaikas. Beim 3:1-Sieg der Reggae Boyz über Trinidad und Tobago kam Smith von Spielbeginn an und über die vollen 90 Minuten zum Einsatz. Nach einem weiteren Freundschaftsspieleinsatz im September 2010 gegen Costa Rica holte ihn Whitemore rund zwei Monate später für ein Vorbereitungsspiel auf die Karibikmeisterschaft 2010, abermals gegen Costa Rica, in den jamaikanischen 22-Mann-Kader. Danach war er ebenfalls während des besagten Turniers, das 26. November bis 5. Dezember 2010 auf Martinique ausgetragen wurde, Stammspieler in der jamaikanischen Nationalmannschaft. Während der Endrunde kam Smith in zwei der drei Gruppenspiele seines Teams zum Einsatz und war nach dessen Sieg in der Gruppe I auch im nachfolgenden Halbfinalspiel gegen Grenada, das in einem 2:1-Sieg Jamaikas nach der Verlängerung endete, im Einsatz, als er in Minute 72 für Shaun Francis auf den Rasen kam und in der 97. Spielminute den entscheidenden Treffer für sein Heimatland erzielte. Im anschließenden Finale gegen Guadeloupe, das Jamaika erst im Elfmeterschießen für sich entscheiden konnte, spielte Smith über die volle Spieldauer durch und erzielte dabei auch das letzte Elfmetertor seiner Mannschaft, ehe der ihm nachfolgende Jean-Luc Lambourde aus Guadeloupe seinen Elfmeter vergab.

Nach dem Erfolg bei der Karibikmeisterschaft holte ihn Whitmore im März 2011 für ein Freundschaftsspiel gegen Venezuela in den Nationalkader und setzte ihn danach erst wieder rund ein halbes Jahr später in einem freundschaftlichen Länderspiel gegen Ecuador ein. Den CONCACAF Gold Cup 2011, für den sich die Reggae Boyz aufgrund ihres Sieges in der Karibikmeisterschaft qualifiziert hatten, verpasste Smith und gehörte nicht einmal zum erweiterten Kader. Danach holte Whitmore den zumeist defensiv eingesetzten Smith im Februar 2012 für ein Trainingscamp mit zwei Freundschaftsspielen gegen Kuba in die Nationalmannschaft. Im ersten Spiel noch nicht im Einsatz, absolvierte der 1,78 m große Akteur die zweite Begegnung mit den Kubanern, als er beim 3:0-Erfolg zur Halbzeit für Ryan Johnson auf den Rasen kam. Wenige später reiste er mit dem jamaikanischen Nationalteam nach Neuseeland und traf dort auf die hiesige Nationalmannschaft. Beim 3:2-Erfolg seines Teams war Smith wieder über die volle Spieldauer auf dem Spielfeld. Smiths Einsatz beim etwa einen Monat später stattfindenden Freundschaftsspiel gegen Costa Rica war zugleich sein letzter Einsatz in der jamaikanischen Fußballnationalmannschaft.

Erfolge
mit Montego Bay United
 Meister der National Premier League: 2013/14
 Vizemeister National Premier League: 2014/15
 Finalist des jamaikanischen Fußballpokals: 2014

mit der jamaikanischen Fußballnationalmannschaft
 Gewinner der Fußball-Karibikmeisterschaft: 2010

Weblinks

 Troy Smith in der CaribbeanFootballDatabase (englisch)

Einzelnachweise

Fußballnationalspieler (Jamaika)
Fußballspieler (Village United FC)
Jamaikaner
Geboren 1987
Mann

redpajama_set_name: RedPajamaWikipedia


text:
Mugena () è una frazione di 141 abitanti del comune svizzero di Alto Malcantone, nel Cantone Ticino (distretto di Lugano).

Geografia fisica

Storia
Nel territorio comunale vi era forse un insediamento romano, del quale restano alcune urne cinerarie. La prima traccia del paese risale però al 1214, quando fu menzionato con il nome di Megiadina, e poi con vari altri nomi nel corso dei secoli (Migena nel 1270, ). Non è più visibile il castrum : della fortezza resta solo una citazione in una pergamena .

Già comune autonomo che si estendeva per 3,7 km², il  2005 è stato accorpato agli altri comuni soppressi di Arosio, Breno, Fescoggia e Vezio per formare il comune di Alto Malcantone.

Monumenti e luoghi d'interesse
 Chiesa parrocchiale di Sant'Agata, attestata dal 1361;
 ;
 ;
 ;
 Rifugio Agario, dotato di due posti letto, a un'altitudine di 1 574 m s.l.m..

Società

Evoluzione demografica
L'evoluzione demografica è riportata nella seguente tabella:

Amministrazione
Ogni famiglia originaria del luogo fa parte del cosiddetto comune patriziale e ha la responsabilità della manutenzione di ogni bene ricadente all'interno dei confini della frazione. .

Note

Bibliografia
 Virgilio Chiesa, Lineamenti storici del Malcantone, Tipografia Gaggini-Bizzozero, Lugano 1961.
 Virgilio Gilardoni, Il Romanico. Catalogo dei monumenti nella Repubblica e Cantone del Ticino, La Vesconta, Casagrande S.A., Bellinzona 1967, 438.
 Plinio Grossi, Il Malcantone, riedizione della Guida Galli-Tamburini, Fontana Print Società Anonima Pregassona 1984, 76-78, 142, 147.
 Bernhard Anderes, Guida d'Arte della Svizzera Italiana, Edizioni Trelingue, Porza-Lugano 1980, 229.
 Giovanni Maria Staffieri, "Mugena", in Malcantone. Testimonianze culturali nei comuni malcantonesi, Lugano-Agno 1985, 73-75.
 Flavio Maggi, Patriziati e patrizi ticinesi, Pramo Edizioni, Viganello 1997.
 Luciano Vaccaro, Giuseppe Chiesi, Fabrizio Panzera, Terre del Ticino. Diocesi di Lugano, Editrice La Scuola, Brescia 2003, 123.
 AA.VV., Guida d'arte della Svizzera italiana, Edizioni Casagrande, Bellinzona 2007, 384, 386, 398.

Altri progetti

Collegamenti esterni

Frazioni di Alto Malcantone
Comuni del Canton Ticino soppressi
Località del Canton Ticino


I am so thrilled to announce that I am a brand new contributor for the Cincinnati Moms Blog! This terrific blog just launched in September, and I actually reached out to the owners (Sarah and Jesika) initially to discuss partnerships and other opportunities in my capacity as a Barefoot Books ambassador.
We met at a location extremely convenient to me and chatted about our kids, the blog, and Barefoot Books. Sarah and Jesika are such sweet, wonderful women, and I am in awe of their vision for the site. Together, we came up with some possible partnership opportunities, which I am extremely excited about! I can't wait to get Barefoot in front of their readers- I know they'll just love them.
During our discussion, they mentioned they had read my blog and wondered if I'd like to be a contributor to their site. I was hopping with glee (internally), and of course I contacted them shortly thereafter to accept! I learned the ground rules, submitted my bio, and tried to jump right in tossing out ideas for content.
My first post actually just went live yesterday, and I am so proud of it! I'd love it if you went and checked it out (Fall Family Traditions)!
I still cannot believe I have gotten this amazing opportunity to be in on the ground floor of such an amazing site. I am so looking forward to watching the blog grow and expand as we continue to spread the word and source great content for our readers. What an exciting time!


Beautiful 2 Story, 3 Sided Brick, Finished Bsmt Home Minutes to Mall of Ga. Highly Ranked Schools, Sought After Swim/Tennis Community. Private Backyard. Exquisite Hardwood Floors and Stunning Trim Throughout. Grand Rm w/ Coffered Ceiling, Stone Frplc, Built Ins & Bowed Windows. Oversized High End Eat In Kitch. Formal Liv & Din Rooms. BR & Full Ba on Main. Upstairs Mstr w/ Frplc & Sit Rm. Lux Ba and Walk In Closet. Great Size Sec Bdrms, Upstairs Media Room. Finished Bsmt Has Rec Rm Plumbed for Kitchen, Media Rm, Bonus/6th BR and Full Ba. Seller is having finished basement and 2 bedrooms upstairs painted same color as rest of the house.


Steve Fletcher, a US marine stationed in Iraq (I think), discovers a nuclear weapon during an inspection. A group of terrorists plan on detonating the bomb in London and realizing Fletcher�s discovery �mark� him for death. Austin Hawke, a british mercenary, is hired to protect Fletcher as he seeks to stop the terrorist plot.
".... The Mark is best left to an afternoon needing to be blasted away with a small dose of fun."
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text:
Town and Country é uma cidade localizada no estado americano do Missouri, no Condado de St. Louis.

Demografia
Segundo o censo americano de 2000, a sua população era de 10.894 habitantes.
Em 2006, foi estimada uma população de 10.773, um decréscimo de 121 (-1.1%).

Geografia
De acordo com o United States Census Bureau tem uma área de 30,8 km², dos quais 30,8 km² cobertos por terra e 0,0 km² cobertos por água.

Localidades na vizinhança
O diagrama seguinte representa as localidades num raio de 8 km ao redor de Town and Country.

Ligações externas

Cidades do Missouri
Localidades do condado de St. Louis (Missouri)


In less than a month, it is Valentine's Day—the sweetest time of the year. The first Valentine's Day that Roy (my husband now) and I spent together, we were both poor college students. We went to a school dancing party and at the end, he put a rose in my hand. More than a decade passed, I still vividly remember the aroma of that rose.
Each February 14th, I get some small gifts from Roy. Nothing expensive; just things like a hand-made card (with my children's beautiful drawings), a notebook (I love writing), and a lovely teacup (tea-drinkers can never have enough teacups). I absolutely love those gifts. It is never about how expensive they are, rather how thoughtful they are.
In this post, I'd like to share with you some frugal gift ideas for Valentine's Day. Here are 10 wonderful gift choices for her and all of them are under $15.
Beautiful hand painted Pint size Mason Jar. It will be a nice decoration for home office, family room, or bedroom.
This is a perfect gift for candle lovers. This candle is handmade and scented with your choice of fragrance. Best of all, the seller can customize the lid with any name or short sentence at no additional cost.
Each mug is custom made to order. The cup is Microwave and dishwasher safe. The design is permanently printed on one side of the mug – not a sticker or vinyl.
A cool hand care kit with 3 popular Burt's Bees hand care products, including Almond Milk Hand Cream, Lemon Butter Cuticle Cream, and Shea Butter Hand Repair Cream, plus 1 pair of cotton gloves.
This mini mailbox bank is just too cute to pass. Use it as a sweet decoration and a nice place to store your coins. It even comes with two tiny keys.
With thick lined paper and vintage leather, this journal makes writing a pleasant experience. Small enough to be put in a purse and easy enough to jot down ideas and thoughts.
This beautiful scarf with gorgeous color is made from soft cotton. It creates feminine, fashionable looks and can be a perfect accent to any outfit.
This Salt Scrub is 100% pure and natural body scrub, with a high-quality Himalayan salt for its maximum nutrient profile. It helps improve hydration and mineral status of the body.
This soap gift box sampler contains nine 25-gram guest soaps in wonderful smelling scents. It comes in a beautiful gift box.
What do you think about these frugal gift ideas for her? Check out the post on Valentine's gifts under $15 for him.
I love all the gifts on the list and would be happy to give ( or receive) any item on this list any time of year, not just on Valentine's day! 🙂 Thoughtfulness is romantic any time of year.
Thanks! It is not the gift itself, but the thoughtfulness in it!


text:
Каср-Амра (), часто Кусейр-Амра або Кусайр-Амра, є найвідомішою з фортець пустелі, що розташована в сучасній східній Йорданії.

Побудований на початку VIII століття, цей комплекс будівель в пустелі був одночасно фортецею зі своїм гарнізоном та резиденцією халіфів із династії Омейядів. Найціннішими в цьому прекрасному невеликому палаці є зал прийомів і лазня — «хаммам». Обидві будови багато прикрашені фігурними розписами, що представляють світське мистецтво того часу.

Приблизно в 40 км на захід від Ель-азрака знаходиться замок Каср-Амра, побудований між 705 і 715 рр. за наказом халіфа Валіда I.

Це порівняно невеликий мисливський палац з маленькими, але численними залами і кімнатами, стіни яких місцями зовсім прикрашені ретельно виконаними фресками, що робить його цікавим зразком середньовічного мистецтва.

Примітки

Посилання
 Christian Sahner, "Snapshot of a Civilization in the Making," The Wall Street Journal, 27 November 2010
 UNESCO World Heritage Site listing
 Qusayr 'Amra, Archnet Digital Library

Світова спадщина в Йорданії
Споруди, збудовані у VIII столітті
Природоохоронні об'єкти, засновані 1985


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Coaches know when you are tired in training thanks to this wearable tracker!
You might have seen athletes, men & women, wearing something that looks like a sports bra during training.
Those are actually the tracking devices the title speaks of.
Catapult, developed out of the Australian Institute of Sport (AIS) for multi-sport use, has been used in over 30 sports at the elite level. They are pioneers in the field of Sports Science, the graph below shows every 'world first' innovation utilised in Catapult.
Some of the early adopters of the Catapult system have been football and rugby teams. More recently 30 American football college teams and 15 NFL teams have signed up.
The system includes a sensor that weighs 85 grams contained in a vest worn by an athlete during training, that measures biomechanical data transferred in real time to the coach's laptop.
Whether he moved faster when he went one way or the other.
The monitor can detect even a slight change in a player's gait, which can be a sign of fatigue or injury.
"College teams using the system have reported an average of a 27-percent decrease in soft-tissue injuries." – Catapult sports performance manager Ben Peterson.
When an athlete does get hurt, sports medicine personnel can use Catapult data to manage his recovery. For instance, if an athlete only reaches 70 percent of his maximum speed, you can say that he isn't ready for a full game yet.
Coaches can see which players are working as hard as they can and, conversely, identify ones who aren't.
With sports tracking reaching the level it has so far, it makes sense when we see simpler fitness trackers make its way into mainstream consumer markets, with products like the Jawbone Up24 and the Fitbit Surge.
Fitness tracking is the future, and sports science will be leading the charge.


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Execute Chinese drug dealers - Harawira
Cleo Fraser
Hone Harawira. Credits: Getty
Mana leader Hone Harawira has called for capital punishment for Chinese people who import methamphetamine into New Zealand.
Appearing on The Nation on Saturday, the former MP said it's time to take the fight against meth seriously by targeting what he says is its source - China.
"We can pass a law to say any Chinese who bring meth or its precursors into this country is either going to jail forever, is going to get sent back and never be allowed here again, or is going to get executed," he told host Lisa Owen.
"We need to send a message this is unacceptable."
Asked if his execution policy extended to gangs, Mr Harawira said "even the police will admit the gangs don't actually do all the meth here".
He said the policy could eventually cover other nationalities, but "you've got to start somewhere".
He denied the policy was racist.
"You want to know what's racist? Maori are in the bottom of New Zealand society in terms of housing, employment, education, health and justice. Now that's what I call racist, in this country."
Labour MP Chris Hipkins wasted no time, slamming Mr Harawira on Twitter as the interview was still on air.
"Even Donald Trump at the height of his anti-China narrative didn't suggest an ethnically targeted death penalty," Mr Hipkins said.

redpajama_set_name: RedPajamaCommonCrawl


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Crisis-hit Lebanon names new government
BEIRUT (AFP) – Lebanon ended a painful wait by unveiling a new Cabinet line-up, but the government was promptly scorned by protesters and faces the Herculean task of saving a collapsing economy.
More than a month after he was designated with backing from Hezbollah and nearly three after his predecessor Saad Hariri resigned under pressure from the street, Prime Minister Hassan Diab on Tuesday announced his Cabinet of 20 ministers.
The academic and former education minister, who was little-known in Lebanon until last month, insisted in his first comments as Premier that his Cabinet was a technocratic one that would strive to meet protesters' demands.
"This is a government that represents the aspirations of the demonstrators who have been mobilised nationwide for more than three months," he said.
He said his government "will strive to meet their demands for an independent judiciary, for the recovery of embezzled funds, for the fight against illegal gains".
Lebanese President Michel Aoun heads the first meeting of Prime Minister Hassan Diab's newly constituted government at the presidential palace in Baabda east of the capital Beirut. PHOTO: AFP
Groups of demonstrators had gathered in the streets of Beirut before the Cabinet was even unveiled, blocking off a main street in the centre of the capital where violent scuffles with the police left dozens wounded over the weekend.
Close to the parliament building, protesters attempted to rip down barbed wire and throw stones at police, who responded with tear gas and water cannon, an AFP journalist witnessed.
The government includes the country's first-ever female Defence Minister, Zeina Akar, and five other women.
The post of Foreign Minister, which had been held by President Michel Aoun's controversial son-in-law Gebran Bassil, was handed to respected diplomat Nassif Hitti.
The new Cabinet is made up of unfamiliar figures, many of them academics and former advisers, but protesters were quick to argue that the absence of the biggest names in Lebanon's widely reviled hereditary political elite was but a smokescreen.
"We want a new Lebanon, a Lebanon with no corruption," Charbel Kahi, a 37-year-old farmer, told AFP as fellow protesters beat drums behind him.
"They are not taking the Lebanese people seriously with this government," he said.
Diab admitted that "Lebanon is experiencing a difficult time in its history" and called for stability but within minutes of his address protesters were out in the streets of several cities, including Tripoli, Sidon and Byblos.
Professor at the American University of Beirut Hilal Khashan argued that the idea of a genuinely technocratic government in Lebanon was "wishful thinking".
"Behind every candidate, there is a political party backing their nomination," he said.
Paula Yacoubian, a former journalist and independent Member of Parliament (MP), scorned the new line-up as "patches on old clothes".
"Hassan Diab did not keep his promise of forming a government of independent" experts," she said.
Diab, a 61-year-old engineering professor at the American University of Beirut and self-professed technocrat, had come under pressure on both the political and economic fronts.
Every day that passed without a Cabinet had fuelled the anger of protesters and tested the patience of foreign donors warning that the quasi-bankrupt state could ill afford further delays.
Donors and citizens are pinning their hopes on a new government to spearhead reforms, unlock billions in international aid and help stabilise a plummeting currency.
"The task that awaits any Cabinet during this serious period is Herculean," said political scientist Karim Mufti.
"In view of the multidimensional nature of the crisis, it seems difficult to envisage short-term solutions to the country's financial, economic and social problems."
A grinding dollar liquidity crisis and informal caps on withdrawals of the greenback have compounded them crisis, leaving Lebanon on the brink of default.
The outgoing government included all of Lebanon's political factions, but Hariri's Sunni-dominated movement and some of his allies have opted to stay out of the new Cabinet.
This leaves the small country of six million led by a government dominated by the sanctions-hit Hezbollah movement and its allies.
Both the Christian bloc of President Michel Aoun and the Shiite Amal party of Parliament Speaker Nabih Berri are political allies of the Iran-backed organisation.
Observers have warned that such a lopsided government could struggle to foster enough goodwill at home and abroad to implement much-needed reforms.
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We used some great drums to capture the essence of a modern maple kit. Maple kits are the most versatile drum kits around and used by many professional drummers for all kinds of music styles.
Known for their warmth, sustain, resonance, high mid-range and low-end punch, this kit sounds great for most applications. Many drummers describe maple as having a warmer tone.
The same kit was also recorded with different microphones, with muting, tricked out heads and a piccolo side snare along with studio gobos and a curtain to deaden the sound to create a more urban style kit.
The oak kit had a much quicker attack and quick decay than the maple kit, yet there was plenty of warm tone coming from the shells.
Oak kits offer different characteristics in tone and timbre than maple.
Everyone knows these kits. They normally come in a 4-piece configuration dating back to the '60s and used by players for early rock and pop songs as well as psychedelic classics.
The 3 ply shells have a warm tone with a smooth, even sustain. The kick is a bit thumpier than modern maple kits giving it more a low-mid presence that has unmistakable familiarity.
To get another characteristic sound with this kit we muted down the drums with tea towels and used some vintage mics and compressors to get the classic sound used in the studio for many albums in the '60s. Notably around Abbey Road in London.
These kits were big in tracks from the '70s and '80s. Very often drummers would put pinstripe heads on the drums to maximize the tonal range for a round and deep tone with lots of projection.
Birch drums are known for their quick attack volume and bright sound and can be used for many types of applications with a wide variety of drum sizes and configurations.
We also got the '90s big kit sound by combining several kick drum shells together to create a "drum tunnel" and running the sound through a sub mic.
The sound was so big in the control room that the walls shook!
Known for their exotic wood shells bubinga drums are known for their aggressive attack, full deep, dark tone with powerful resonance and rich sustain.
Many drummers love the punchy, lush, natural tone of bubinga.
These kits are fairly esoteric due to their lack to subtlety. Known for being loud and proud.
Most drummers use these drums to be noticed and can be found on classic prog rock and heavy metal songs.
These are great kits to experiment for something different in tone, volume and presence in your songs.
These kits are notorious for their big sound and strong attack. These have a hard sound with very little resonance.
This kit has a particularly large kick drum (24″). It has a big, boomy sound that recaptures the bottom end of many classic '70s tracks.
This kit from the '50s has a gorgeous sound reminiscent of many jazz drummers.
The super-warm tone and resonant gum-maple shells has a complex tone and timbre that compliments your playing.
A unique kit with a bright and dry tone compared to maple.
Mahogany is known for its low-end punch. With less projection than birch or maple you get the trade off with a warmer and softer tone.
This kit has a nice warm responsiveness with enhanced resonance that it brings to the forefront when playing funk or rock tunes.
Most drummers have more than one snare for sonic versatility. The material, size and head can completely affect the characteristic of a snare drum.
We sought out a wide collection of classic snares in various sizes as well as shell types. We also sampled the snares with sticks, brushes in various zones to capture the nuance of its sound.
The complex timbre of various cymbals plus the brand, size and thickness of all the cymbal types can seem endless for hi-hats, crashes and rides.
We sought the major brands of cymbals and recorded them as sets for consistency. We also grabbed china cymbals, rivet cymbals, and plenty of splashes to round out the sound set to cover most drummers needs.