Evolution of the $f\sigma_8$ tension with the Planck15/$\Lambda$CDM
  determination and implications for modified gravity theories
  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 ($g_a\neq 0$).
