Evolution of the f σ 8 tension with the Planck 15 / Λ CDM determination and implications for modified gravity theories

摘要: We construct an updated extended compilation of distinct (but possibly correlated) $f{\ensuremath{\sigma}}_{8}(z)$ redshift space distortion (RSD) data published between 2006 and 2018. It consists 63 datapoints is significantly larger than previously used similar sets. After fiducial model correction we obtain the best fit ${\mathrm{\ensuremath{\Omega}}}_{0m}\ensuremath{-}{\ensuremath{\sigma}}_{8}$ $\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ parameters show that they are at a $5\ensuremath{\sigma}$ tension with corresponding $\text{Planck}15/\mathrm{\ensuremath{\Lambda}}\mathrm{CDM}$ values. Introducing nontrivial covariance matrix correlating randomly 20% RSD has no significant effect on above level. disappears (becomes less $1\ensuremath{\sigma}$) when subsample 20 most recently used. A partial cause for this reduced fact more recent tend to probe higher redshifts (with errorbars) where there degeneracy among different models due matter domination. Allowing evolution effective Newton's constant as ${G}_{\mathrm{eff}}(z)/{G}_{\mathrm{N}}=1+{g}_{a}{(\frac{z}{1+z})}^{2}\ensuremath{-}{g}_{a}{(\frac{z}{1+z})}^{4}$ (${g}_{a}$ parameter) fixing background find ${g}_{a}=\ensuremath{-}0.91\ifmmode\pm\else\textpm\fi{}0.17$ from full $f{\ensuremath{\sigma}}_{8}$ set while earliest latest imply ${g}_{a}=\ensuremath{-}{1.28}_{\ensuremath{-}0.26}^{+0.28}$ ${g}_{a}=\ensuremath{-}0.4{3}_{\ensuremath{-}0.41}^{+0.46}$ respectively. Thus, appear favor GR in contrast earlier data. Finally, parametrization $f{\ensuremath{\sigma}}_{8}(z)=\ensuremath{\lambda}{\ensuremath{\sigma}}_{8}\mathrm{\ensuremath{\Omega}}(z{)}^{\ensuremath{\gamma}}/(1+z{)}^{\ensuremath{\beta}}$ provides excellent solution growth equation both (${g}_{a}=0$) modified gravity (${g}_{a}\ensuremath{\ne}0$).