Testing Quasi-Linear Coasting Cosmologies with Late-Time Large-Scale Structure Growth

TL;DR

This study tests quasi-linear coasting cosmologies against late-time large-scale structure data, comparing their fit and predictive power to the standard Lambda-CDM model, and examines their potential to resolve the S8 tension.

Contribution

It provides analytical expressions for growth factors in coasting models, fits these models to data, and compares their statistical performance and tension resolution capabilities with Lambda-CDM.

Findings

All models fit the data well, but Lambda-CDM is statistically favored.

Coasting models show higher S8 values, reducing tension with Planck data.

Lambda-CDM achieves higher predictive accuracy but may overfit.

Abstract

We derive analytical expressions for the growth factor, $D(z)$, and density-weighted growth rate, $f\sigma_8(z)$, for cosmologies in which $a\propto t$ at late times. We fit $f\sigma_8(z)$ to data from redshift-space distortion measurements in the redshift range $z<2$ using the `dynesty` implementation of nested sampling. Three coasting models, with curvature parameters $k=\{-1, 0, +1\}$ in $H^2_0c^{-2}$ units, and a flat $\Lambda$CDM model are tested. We evaluate each model's consistency with the data by applying the Anderson--Darling test for normality on the normalized residuals. We obtained $\Omega_\mathrm{m,0}=\{ 0.206^{+0.073}_{-0.061},\, 0.297^{+0.085}_{-0.073},\, 0.412^{+0.097}_{-0.086}\}$} and $\sigma_{8}(z=0)=\{1.071^{+0.213}_{-0.151},\,0.867^{+0.128}_{-0.097},\,0.725^{+0.080}_{-0.065}\}$ for the coasting models, while for $\Lambda$CDM $\Omega_\mathrm{m,0}=0.286_{-0.047}^{+0.053}$ and $\sigma_{8}(z=0) = 0.764_{-0.035}^{+0.039}$. All models are consistent with the data, though the $\Lambda$CDM model is strongly favored over the coasting models, with $\log$ Bayes factors of $\log_{10}{\mathcal{B}} = \{1.79,\, 1.55,\,1.42\}$. A predictive performance metric and posterior predictive check confirmed that while $\Lambda$CDM achieves the highest predictive accuracy, it also shows the strongest indication of overfitting. We also examined whether the $S_8$ tension can be resolved by linear expansion for $z<2$. Curve fitting yielded $S_8 = \{0.890^{+0.024}_{-0.024},\,0.865^{+0.024}_{-0.024},\,0.850^{+0.026}_{-0.026}\}$ for the coasting models, resulting in $\Delta S^\mathrm{Coasting}_8=\{2.12\sigma,\,1.21\sigma,\,0.62\sigma\}$ discrepancies with the standard \textit{Planck} 2018 value. A value of $S_8=0.746^{+0.041}_{-0.039}$ was obtained for the $\Lambda$CDM model, indicating a tension level of ${\Delta S_8^{\Lambda\mathrm{CDM}}=2.00\sigma}$.