Observational analysis of late-time acceleration in $f(Q, L_m)$ 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 $f(Q)$ 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 $\alpha$, $\beta$, and $n$ are constants. The derived Hubble parameter $H(z) = H_0 (1+z)^{\frac{3n}{2(2n-1)}}$ indicates that $n$ significantly influences the scaling of $H(z)$ 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 $H(z)$ 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 $\Lambda$CDM 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 $\Lambda$CDM.