Growth Rate Analysis in $f(R,L_m)$ Gravity: A Comparative Study with \boldmath$\Lambda$CDM Cosmology

TL;DR

This study explores how modified gravity theories with non-minimal matter coupling affect cosmic structure growth, comparing their predictions with the standard $\\Lambda$CDM model using recent galaxy survey data.

Contribution

It introduces a detailed analysis of $f(R, L_m)$ gravity's impact on structure formation and compares its predictions with observational data, highlighting potential deviations from $\\Lambda$CDM.

Findings

$f(R, L_m)$ models can fit current data with subtle deviations.

$\\Lambda$CDM remains consistent but less flexible.

Future surveys could distinguish between models.

Abstract

We investigate the evolution of cosmic structures within the framework of modified gravity, specifically focusing on theories described by the function $f(R, L_m)$, where $R$ is the Ricci scalar and $L_m$ is the matter Lagrangian. This class of models introduces a non-minimal coupling between geometry and matter, leading to modifications in the dynamics of density perturbations. We derive the linear growth equation and compute the observable growth rate $f\sigma_8(z)$, which is directly accessible from redshift-space distortion (RSD) data. Using recent observational constraints from galaxy surveys such as eBOSS and DESI, we perform a comparative analysis between predictions from $f(R, L_m)$ gravity and the standard $\Lambda$CDM model. Our results indicate that while $\Lambda$CDM remains broadly consistent with current data, the $f(R, L_m)$ framework can accommodate subtle deviations in structure growth, offering a possible resolution to existing tensions in large-scale structure observations. We also outline the implications of our findings for future surveys, including Euclid and LSST.