Growth Rate Analysis in \(\boldsymbol{f(R,L_{m})}\) Gravity: A Comparative Study with \(\boldsymbol{\Lambda}\)CDM Cosmology

Abstract

We investigate the growth of cosmic structures within the framework of modified gravity described by the functional form \(f(R,L_{m})\), where \(R\) is the Ricci scalar and \(L_{m}\) the matter Lagrangian. This class of models introduces a nonminimal coupling between matter and curvature, leading to modifications in both the background dynamics and the evolution of linear density perturbations. We derive the modified Friedmann equations, obtain an explicit expression for the Hubble parameter \(H(z)\), and formulate a corrected linear growth equation with properly defined effective gravitational coupling \(G_{\text{eff}}\). The observable quantity \(f\sigma_{8}(z)\) is then computed and compared with 23 redshift-space distortion (RSD) measurements from major surveys including 6dFGS, BOSS, eBOSS, WiggleZ, VIPERS, and FastSound. The model parameters are constrained using a combined analysis of Hubble parameter data, Pantheon\({}^{+}\) supernovae, DESI BAO, and the Planck 2018 CMB shift parameter, employing chi-square minimization and MCMC sampling. The results show that the \(f(R,L_{m})\) model fits the growth data slightly better than \(\Lambda\)CDM, particularly at intermediate and high redshifts, while naturally predicting a mild suppression of late-time structure growth. This feature helps alleviate the \(\sigma_{8}\) tension between low- and high-redshift observations. Our findings highlight the consistency of \(f(R,L_{m})\) gravity with current cosmological datasets and underscore its potential as a viable alternative to \(\Lambda\)CDM. We also discuss prospects for constraining such matter-curvature coupling models with future high-precision surveys such as Euclid and LSST.