Evolution of the $f\sigma_8$ tension with the Planck15/$\Lambda$CDM determination and implications for modified gravity theories

TL;DR

This study compiles and analyzes $f\sigma_8(z)$ RSD data from 2006-2018, revealing a tension with Planck15/$\Lambda$CDM that diminishes with recent data and exploring implications for modified gravity through effective Newton's constant evolution.

Contribution

It provides an extensive updated dataset of RSD measurements, assesses the $f\sigma_8$ tension with Planck15/$\Lambda$CDM, and investigates modified gravity effects via evolving Newton's constant.

Findings

Significant $5\sigma$ tension with Planck15/$\Lambda$CDM using the full dataset.

Tension reduces to less than $1\sigma$ when considering only recent data.

Recent data favor General Relativity over modified gravity models.

Abstract

We construct an updated extended compilation of distinct (but possibly correlated) $f\sigma_8(z)$ Redshift Space Distortion (RSD) data published between 2006 and 2018. It consists of 63 datapoints and is significantly larger than previously used similar datasets. After fiducial model correction we obtain the best fit $\Omega_{0m}-\sigma_8$ $\Lambda$CDM parameters and show that they are at a $5\sigma$ tension with the corresponding Planck15/$\Lambda$CDM values. Introducing a nontrivial covariance matrix correlating randomly $20\%$ of the RSD datapoints has no significant effect on the above tension level. We show that the tension disappears (becomes less than $1\sigma$) when a subsample of the 20 most recently published data is used. A partial cause for this reduced tension is the fact that more recent data tend to probe higher redshifts (with higher errorbars) where there is degeneracy among different models due to matter domination. Allowing for a nontrivial evolution of the effective Newton's constant as $G_{\textrm{eff}}(z)/G_{\textrm{N}} = 1 + g_a \left(\frac{z}{1+z}\right)^2 - g_a \left(\frac{z}{1+z}\right)^4$ ($g_a$ is a parameter) and fixing a \plcdm background we find $g_a=-0.91\pm 0.17$ from the full $f\sigma_8$ dataset while the 20 earliest and 20 latest datapoints imply $g_a=-1.28^{+0.28}_{-0.26}$ and $g_a=-0.43^{+0.46}_{-0.41}$ respectively. Thus, the more recent $f\sigma_8$ data appear to favor GR in contrast to earlier data. Finally, we show that the parametrization $f\sigma_8(z)=\lambda \sigma_8 \Omega(z)^\gamma /(1+z)^\beta$ provides an excellent fit to the solution of the growth equation for both GR ($g_a=0$) and modified gravity ($g_a\neq 0$).