The cosmology of $f(R,L_m)$ gravity: constraining the background and perturbed dynamics

This paper delves into the late-time accelerated expansion of the universe and the evolution of cosmic structures within the context of a specific $f(R,L_m)$ gravity model, formulated as $f(R,L_m)=\lambda R+\beta L_m^{\alpha }+\eta$. To study the cosmological viability of the model, we employed the latest cosmic measurement datasets: i) 57 observational Hubble parameter data points ($\mathtt{\text{OHD}}$); ii) 1048 distance moduli data points ($\mathtt{\text{SNIa}}$); iii) a combined dataset ($\mathtt{\text{OHD+SNIa}}$); and large scale structure datasets, including iv) 14 growth rate data points ($\mathtt{\text{f}}$); and v) 30 redshift space distortion data points ($\mathtt{\text{f}}$${\sigma }_8$). These datasets facilitated the constraint of the $f(R,L_m)$-gravity model via MCMC simulations, followed by a comparative analysis with the $\mathrm{\Lambda }$CDM model. A comprehensive statistical analysis has been conducted to evaluate the $f(R,L_m)$-gravity model’s efficacy in explaining both the accelerated expansion of the universe and the growth of cosmic structures.