Linear matter density perturbations in the $\hat{I}{›}_{\mathrm{s}}$CDM model: Examining growth dynamics and addressing the $S_8$ tension

Abstract

We investigate linear matter density perturbations in the $\hat{I}{›}_{\mathrm{s}}$CDM, in which the $\hat{I}›$ is replaced by late-time ($z\sim 2$) 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 $f=\hat{I}{\text{c◯}}_{\mathrm{m}}^3$ and growth index ${\hat{I}}^3$ in both models. Prior to the transition, the AdS-like $\hat{I}›$ reduces cosmic friction, causing linear matter density perturbations to grow more rapidly than in $\hat{I}›$CDM; this effect is most pronounced just before the transition, with a growth rate around $15\%$ higher than $\hat{I}›$CDM around $z\sim 2$. After the transition, $\hat{I}{›}_{\mathrm{s}}$CDM behaves similarly to $\hat{I}›$CDM but features a larger cosmological constant, leading to higher $H(z)$ and greater cosmic friction that more effectively suppresses growth. Before the transition, ${\hat{I}}^3$ remains below both the $\hat{I}›$CDM and EdS values (${\hat{I}}^3\approx 6/11$); during the transition, it increases rapidly and then grows gradually, paralleling $\hat{I}›$CDM while remaining slightly higher in the post-transition era-though overall, it stays near ${\hat{I}}^3\sim 0.55$. Using the Planck best-fit values, $\hat{I}{\text{c◯}}_{m0}=0.28$ for $\hat{I}{›}_{\mathrm{s}}$CDM and $\hat{I}{\text{c◯}}_{m0}=0.32$ for $\hat{I}›$CDM, we find $f=0.49$ and $f=0.53$, respectively. $\hat{I}{›}_{\mathrm{s}}$CDM predicts a value of $f=0.48$, recently obtained from LSS data when ${\hat{I}}^3$ is treated as a free parameter in $\hat{I}›$CDM. This suggests that $\hat{I}{›}_{\mathrm{s}}$CDM may resolve the structure growth anomaly, without deviating from ${\hat{I}}^3\sim 0.55$.

35 pages, 13 figures, 6 tables, matches the version published in JCAP