Growth of structures and redshift-space distortion data in scale-dependent gravity

TL;DR

This paper investigates how scale-dependent gravity affects cosmic structure growth and redshift-space distortions, aiming to resolve tensions in $\sigma_8$ measurements within cosmological observations.

Contribution

It introduces a model where both Newton's constant and the cosmological constant vary with time, analyzing their impact on density perturbations and observational data fit.

Findings

Scale-dependent gravity can reduce the $\sigma_8$ tension.

The model fits supernovae and redshift-space distortion data well.

Predicted $\sigma_8$ values align with observations.

Abstract

This study is devoted to the implications of scale-dependent gravity in Cosmology. Redshift-space distortion data indicate that there is a tension between $\Lambda$CDM and available observations as far as the value of the rms density fluctuation, $\sigma_8$, is concerned. It has been pointed out that this tension may be alleviated in alternative theories in which gravity is weaker at red-shift $z \sim 1$. We study the evolution of density perturbations for non-relativistic matter on top of a spatially flat FLRW Universe, and we compute the combination $A=f \sigma_8$ in the framework of scale-dependent gravity, where both Newton's constant and the cosmological constant are allowed to vary with time. Upon comparison between available observational data (supernovae data as well as redshift-space distortion data) and theoretical predictions of the model, we determine the numerical value of $\sigma_8$ that best fits the data.