Tension and constraints on modified gravity parametrizations of $G_{\textrm{eff}}(z)$ from growth rate and Planck data

Understand

We construct an updated and extended compilation of growth rate data consisting of 34 points and including corrections for model dependence.

• In order to maximize the independence of the datapoints we also construct a subsample of this compilation (`Gold' growth dataset) which consists of 18 datapoints.
• We test the consistency of this dataset with the best fit Planck15/$\Lambda$CDM parameters in the context of General Relativity (GR) using the evolution equation for the growth factor $\delta(a)$ with a $w$CDM background.
• We find tension at the $\sim 3 \sigma$ 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/$\Lambda$CDM parameters.