Weak gravity on a $\Lambda$CDM background

Abstract

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 $\mu \equiv G_{\mathrm{growth}}/G$, $\Sigma \equiv G_{\mathrm{lensing}}/G$ 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 $\mu \ge \Sigma$ at all times. Taking into account the $f{\sigma }_8$ and $E_G$ data constrains the parameter $s$ to satisfy $s\lesssim 2$. Hence these data select essentially the weak gravity regime today (${\mu }_0<1$) when $s<2$, while ${\mu }_0>1$ subsists only marginally for $s\approx 2$. At least the interval $0.5\lesssim s\lesssim 2$ 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 ${\gamma }_0\equiv \gamma {|}_{z=0}$ and ${\gamma }_1\equiv \frac{\mathrm{d}\gamma }{\mathrm{dz}}{|}_{z=0}$. 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.

14 pages, 2 figures

References in corpus (20)

• GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
• Gravitational Waves and Gamma-rays from a Binary Neutron Star Merger: GW170817 and GRB 170817A
• An Ordinary Short Gamma-Ray Burst with Extraordinary Implications: Fermi-GBM Detection of GRB 170817A
• INTEGRAL Detection of the First Prompt Gamma-Ray Signal Coincident with the Gravitational Wave Event GW170817
• Horndeski theory and beyond: a review
• Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity
• Matter density perturbations and effective gravitational constant in modified gravity models of dark energy
• KiDS-450 + 2dFLenS: Cosmological parameter constraints from weak gravitational lensing tomography and overlapping redshift-space galaxy clustering
• The Clustering of the SDSS Main Galaxy Sample II: Mock galaxy catalogues and a measurement of the growth of structure from Redshift Space Distortions at $z=0.15$
• Anisotropic stress as signature of non-standard propagation of gravitational waves
• A unifying description of dark energy
• Observables and unobservables in dark energy cosmologies
• Beyond BAO: improving cosmological constraints from BOSS with measurement of the void-galaxy cross-correlation
• Growth rate of cosmological perturbations at z ~ 0.1 from a new observational test
• 2MTF VI. Measuring the velocity power spectrum
• Generalized Brans-Dicke theories
• The Redshift Space Momentum Power Spectrum II: measuring the growth rate from the combined 2MTF and 6dFGSv surveys
• Cosmological constant vis-a-vis dynamical vacuum: bold challenging the $\Lambda$CDM
• When is the growth index constant?
• Geometric and growth rate tests of General Relativity with recovered linear cosmological perturbations

Cited by in corpus (1)

• A $w-M$ phantom transition at $z_t<0.1$ as a resolution of the Hubble tension