Tension and constraints on modified gravity parametrizations of Geff(z) from growth rate and Planck data

We 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=ACDM parameters in the context of General Relativity using the evolution equation for the growth factor delta(a) with a wCDM background. We find tension at the similar to 3 sigma level between the best-fit parameters w (the dark energy equation of state), Omega(0m) (the matter density parameter), and sigma 8 (the matter power spectrum normalization on scales 8h(-1) Mpc) and the corresponding Planck15=.CDM parameters (w = -1, Omega(0m) = 0.315, and sigma 8 = 0.831). We show that the tension disappears if we allow for evolution of the effective Newton constant, parametrized as G(eff)(a)/G(n) = 1 + g(a)(1 - a)(2n) with n >= 2 where g(a) 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 (G(eff) > 0), b) consistency with big bang nucleosynthesis constraints (G(eff) (a << 1)/G(n),= 1, and c) consistency with Solar System tests (G(eff)(a = 1)/G(N) = 1 and G'(eff) (a = 1)/G(N) = 0). We show that the best-fit form of G(eff) (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 G(eff) (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 3 sigma tension with the corresponding decreasing best-fit G(eff) (z) obtained from the growth data.