Tension and constraints on modified gravity parametrizations of Geff(z) from growth rate and Planck data
AbstractWe construct an updated and extended compilation of growth-rate data based on recent redshift-space distortion measurements. The data set consists of 34 data points and includes corrections for model dependence. In order to minimize overlap and maximize the independence of the data points, we also construct a subsample of this compilation (a “gold” growth data set) which consists of 18 data points. We test the consistency of this data set with the best-fit Planck15/ΛCDM parameters in the context of General Relativity using the evolution equation for the growth factor δ(a) with a wCDM background. We find tension at the ∼3σ level between the best-fit parameters w (the dark energy equation of state), Ω0m (the matter density parameter), and σ8 (the matter power spectrum normalization on scales 8h-1 Mpc) and the corresponding Planck15/ΛCDM parameters (w=-1, Ω0m=0.315, and σ8=0.831). We show that the tension disappears if we allow for evolution of the effective Newton constant, parametrized as Geff(a)/GN=1+ga(1-a)n-ga(1-a)2n with n≥2 where ga and n are parameters of the model, a is the scale factor, and z=1/a-1 is the redshift. This parametrization satisfies three important criteria: a) positive energy of the graviton (Geff>0), b) consistency with big bang nucleosynthesis constraints (Geff(a≪1)/GN=1), and c) consistency with Solar System tests (Geff(a=1)/GN=1 and Geff′(a=1)/GN=0). We show that the best-fit form of Geff(z) obtained from the growth data corresponds to weakening gravity at recent redshifts (decreasing function of z), and we demonstrate that this behavior is not consistent with any scalar-tensor Lagrangian with a real scalar field. Finally, we use MGCAMB to find the best-fit Geff(z) obtained from the Planck cosmic microwave background power spectrum on large angular scales and show that it is a mildly increasing function of z, in 3σ tension with the corresponding decreasing best-fit Geff(z) obtained from the growth data.