Linear matter density perturbations in the $\Lambda_{\rm s}$CDM model: Examining growth dynamics and addressing the $S_8$ tension

TL;DR

This paper explores how a modified $ m extit{s}$CDM model with a late-time transition affects matter growth, potentially resolving the $S_8$ tension by altering growth dynamics and the growth index $oldsymbol{ extgamma}$.

Contribution

It introduces a $ m extit{s}$CDM model with a late-time transition, deriving analytical growth solutions, and shows its potential to resolve the $S_8$ tension.

Findings

Pre-transition growth rate is ~15% higher than $ m extit{ extLambda}$CDM.

Post-transition, $ m extit{ extLambda}}$sCDM mimics $ m extLambda$CDM but with higher $H(z)$.

Predicted growth rate $f$ aligns with LSS data when $ extgamma$ is free.

Abstract

We investigate linear matter density perturbations in the $\Lambda_{\rm s}$CDM, in which the $\Lambda$ is replaced by late-time ($z\sim2$) mirror AdS-dS transition, resulting in distinct growth dynamics. We use two complementary approaches: (i) determining the initial density contrast and its evolution rate for a given collapse scale factor, (ii) computing the collapse scale factor for a specified initial density contrast and evolution rate. We derive analytical solutions for the growth rate $f=\Omega_{\rm m}^\gamma$ and growth index $\gamma$ in both models. Prior to the transition, the AdS-like $\Lambda$ reduces cosmic friction, causing linear matter density perturbations to grow more rapidly than in $\Lambda$CDM; this effect is most pronounced just before the transition, with a growth rate around $15\%$ higher than $\Lambda$CDM around $z\sim2$. After the transition, $\Lambda_{\rm s}$CDM behaves similarly to $\Lambda$CDM but features a larger cosmological constant, leading to higher $H(z)$ and greater cosmic friction that more effectively suppresses growth. Before the transition, $\gamma$ remains below both the $\Lambda$CDM and EdS values ($\gamma\approx6/11$); during the transition, it increases rapidly and then grows gradually, paralleling $\Lambda$CDM while remaining slightly higher in the post-transition era-though overall, it stays near $\gamma\sim0.55$. Using the Planck best-fit values, $\Omega_{\rm m0}=0.28$ for $\Lambda_{\mathrm{s}}$CDM and $\Omega_{\rm m0}=0.32$ for $\Lambda$CDM, we find $f=0.49$ and $f=0.53$, respectively. $\Lambda_{\rm s}$CDM predicts a value of $f=0.48$, recently obtained from LSS data when $\gamma$ is treated as a free parameter in $\Lambda$CDM. This suggests that $\Lambda_{\rm s}$CDM may resolve the structure growth anomaly, without deviating from $\gamma \sim 0.55$.