Weak gravity on a $Lambda$CDM background. (arXiv:2011.01517v2 [gr-qc] UPDATED)
<a href="http://arxiv.org/find/gr-qc/1/au:+Gannouji_R/0/1/0/all/0/1">Radouane Gannouji</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Perivolaropoulos_L/0/1/0/all/0/1">Leandros Perivolaropoulos</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Polarski_D/0/1/0/all/0/1">David Polarski</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Skara_F/0/1/0/all/0/1">Foteini Skara</a>
We consider Horndeski modified gravity models obeying stability, velocity of
gravitational waves $c_T$ equals $c$ and quasistatic approximation (QSA) on
subhorizon scales. We assume further a $Lambda$CDM background expansion and a
monotonic evolution on the cosmic background of the $alpha$ functions as
$alpha_i= alpha_{i0}~a^s$ where $i=M,B$, $a$ is the scale factor and
$alpha_{i0}$ ($alpha_{M0}, alpha_{B0}$), $s$ are arbitrary parameters. We
show that the growth and lensing reduced (dimensionless) gravitational
couplings $muequiv G_{rm growth}/G$, $Sigmaequiv G_{rm lensing}/G$
exhibit the following generic properties today: $Sigma_0 < 1$ for all viable
parameters, $mu_0<1$ (weak gravity today) is favored for small $s$ while
$mu_0>1$ is favored for large $s$. We establish also the relation $mugeq
Sigma$ at all times. Taking into account the $fsigma_8$ and $E_G$ data
constrains the parameter $s$ to satisfy $slesssim 2$. Hence these data select
essentially the weak gravity regime today ($mu_0<1$) when $s<2$, while
$mu_0>1$ subsists only marginally for $sapprox 2$. At least the interval
$0.5lesssim s lesssim 2$ would be ruled out in the absence of screening. We
consider further the growth index $gamma(z)$ and identify the
$(alpha_{M0},alpha_{B0},s)$ parameter region that corresponds to specific
signs of the differences $gamma_0-gamma_0^{Lambda CDM}$, and
$gamma_1-gamma_1^{Lambda CDM}$, where $gamma_0equiv gammabigl|_{z=0}$
and $gamma_1equiv frac{{rm d}gamma}{rm d z}bigl|_{z=0}$. In this way
important information is gained on the past evolution of $mu$. We obtain in
particular the signature $gamma_0>gamma_0^{Lambda CDM}$ for $s<2$ in the
selected weak gravity region.
We consider Horndeski modified gravity models obeying stability, velocity of
gravitational waves $c_T$ equals $c$ and quasistatic approximation (QSA) on
subhorizon scales. We assume further a $Lambda$CDM background expansion and a
monotonic evolution on the cosmic background of the $alpha$ functions as
$alpha_i= alpha_{i0}~a^s$ where $i=M,B$, $a$ is the scale factor and
$alpha_{i0}$ ($alpha_{M0}, alpha_{B0}$), $s$ are arbitrary parameters. We
show that the growth and lensing reduced (dimensionless) gravitational
couplings $muequiv G_{rm growth}/G$, $Sigmaequiv G_{rm lensing}/G$
exhibit the following generic properties today: $Sigma_0 < 1$ for all viable
parameters, $mu_0<1$ (weak gravity today) is favored for small $s$ while
$mu_0>1$ is favored for large $s$. We establish also the relation $mugeq
Sigma$ at all times. Taking into account the $fsigma_8$ and $E_G$ data
constrains the parameter $s$ to satisfy $slesssim 2$. Hence these data select
essentially the weak gravity regime today ($mu_0<1$) when $s<2$, while
$mu_0>1$ subsists only marginally for $sapprox 2$. At least the interval
$0.5lesssim s lesssim 2$ would be ruled out in the absence of screening. We
consider further the growth index $gamma(z)$ and identify the
$(alpha_{M0},alpha_{B0},s)$ parameter region that corresponds to specific
signs of the differences $gamma_0-gamma_0^{Lambda CDM}$, and
$gamma_1-gamma_1^{Lambda CDM}$, where $gamma_0equiv gammabigl|_{z=0}$
and $gamma_1equiv frac{{rm d}gamma}{rm d z}bigl|_{z=0}$. In this way
important information is gained on the past evolution of $mu$. We obtain in
particular the signature $gamma_0>gamma_0^{Lambda CDM}$ for $s<2$ in the
selected weak gravity region.
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