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

Abstract

We derive analytical expressions for the growth factor, $D(z)$, and density-weighted growth rate, $f\ddot{I}{ƒ}_8(z)$, for cosmologies in which $a\propto t$ at late times. We fit the resulting $f\ddot{I}{ƒ}_8(z)$ predictions to redshift-space-distortion measurements in the range $z<2$ using the `dynesty` implementation of nested sampling. Three coasting models, with curvature parameters $k=\{-1,0,+1\}$ in $H_0^2{c}^{-2}$ units, and a flat $\hat{I}›$CDM model are tested. We evaluate each model's consistency with the data using the Anderson--Darling test for normality applied to the uncertainty-normalised residuals, supplemented by posterior predictive checks. For the coasting models, we obtain $\hat{I}{\text{c◯}}_{\mathrm{m},0}=\{0.206_{-0.061}^{+0.073},0.297_{-0.073}^{+0.085},0.412_{-0.086}^{+0.097}\}$ and $\ddot{I}{ƒ}_8(z=0)=\{1.071_{-0.151}^{+0.213},0.867_{-0.097}^{+0.128},0.725_{-0.065}^{+0.080}\}$, respectively. For $\hat{I}›$CDM, we obtain $\hat{I}{\text{c◯}}_{\mathrm{m},0}=0.286_{-0.047}^{+0.053}$ and $\ddot{I}{ƒ}_8(z=0)=0.764_{-0.035}^{+0.039}$. All models are consistent with the data, although $\hat{I}›$CDM is favoured over the coasting models, with log Bayes factors ${\log }_{10}\mathcal{B}=\{1.79,1.55,1.42\}$. This preference is robust against alternative priors and prior parametrisations, but weakens when heavier-tailed likelihoods are adopted. Predictive performance is assessed using the expected log predictive density computed by leave-one-out cross-validation. The $\hat{I}›$CDM model has the largest predictive performance, but its advantage is statistically significant only relative to the $k=\{-1,0\}$ coasting models.

19 pages, 3 figures; updated Introduction, Discussion, and references to reflect recent developments regarding the S8 tension; clarified the interpretation of model selection and validation metrics