Observational analysis of late-time acceleration in f(Q,Lm) gravity

In this study, we explored late-time cosmology within an extended class of theories based on $f(Q,L_m)$ gravity. This theory generalizes $f\left(Q\right)$ gravity by incorporating a non-minimal coupling between the non-metricity Q and the matter Lagrangian $L_m$, analogous to the $f(Q,T)$ theory. The coupling between Q and $L_m$ leads to the non-conservation of the matter energy-momentum tensor. We first investigated a cosmological model defined by the functional form $f(Q,L_m)=\alpha Q+\beta L_m^n$, where α, β, and n are constants. The derived Hubble parameter $H\left(z\right)=H_0{(1+z)}^{\frac{3n}{2(2n-1)}}$ indicates that n significantly influences the scaling of $H\left(z\right)$ over cosmic history, with $n>2$ suggesting accelerated expansion. We also examined the simplified case of $n=1$, leading to the linear form $f(Q,L_m)=\alpha Q+\beta L_m$, consistent with a universe dominated by non-relativistic matter. Using various observational datasets, including $H\left(z\right)$ and Pantheon, we constrained the model parameters. Our analysis showed that the $f(Q,L_m)$ model aligns well with observational results and exhibits similar behavior to the ΛCDM model. The results, with $q_0=-0.22\pm 0.01$ across all datasets, indicate an accelerating universe, highlighting the model's potential as an alternative to ΛCDM.