Bouncing cosmological models and cosmic acceleration in f(Q,Lm) theory: A path beyond the big bang singularity

Abstract

This manuscript explores bouncing cosmological solutions in the recently developed $f(Q,L_m)$ gravity theory, where $Q$ represents non-metricity and $L_m$ denotes the matter-Lagrangian density. We analyze a spatially flat, homogeneous and isotropic universe with an isotropic matter distribution, considering a specific functional form of $f(Q,L_m)$ to examine its impact on cosmic evolution. By solving the modified field equations, we investigate different bounce models and assess their viability through a detailed analysis of cosmological parameters. Our findings indicate that the energy density remains positive while pressure turns negative near the bounce, with the null energy condition being violated in all models around the bounce point except oscillatory bounce model. This violation is a critical requirement for realizing a non-singular cosmological transition. The effective state parameter shifts from phantom-like values $\omega >-1$ near the bounce to quintessence-like behavior $-1<\omega <-\frac{1}{3}$ at late times, depending on the model parameters. In particular, the symmetric bounce model enters a strong phantom regime signaling cosmic acceleration at late times. These results reinforce the physical viability of stable, singularity-free bounce solutions and suggest that $f(Q,L_m)$ gravity could serve as a promising alternative to inflationary cosmology for describing the early universe dynamics.