Kinematic reconstruction of the late-time expansion history in $f(R, L_m, T)$ gravity from recent cosmological observations

Abstract Within the FLRW framework, we reconstruct the late-time expansion history in $f(R,L_m,T)$ gravity using a redshift-dependent parametrization of the deceleration parameter. Its free parameters are constrained using Cosmic Chronometers~(CC), DESI DR2 baryon acoustic oscillations and Pantheon+ Type Ia supernovae data. The reconstructed expansion history consistently indicates a transition from deceleration to acceleration at $z_{\rm t}\approx0.6$, with the present-day deceleration parameter constrained to $q_0=-0.52$ for both the CC and CC+DESI DR2 combinations and $q_0=-0.50$ for the combined CC+DESI DR2+Pantheon+ dataset. The Statefinder diagnostic reveals a non-monotonic kinematic evolution, with the reconstructed trajectories successively passing through Chaplygin gas-like, $\Lambda$CDM-like and quintessence-like regimes before returning toward the Chaplygin gas-like region near the present epoch. The reconstructed cosmic age is $t_0\approx13.0$--$13.3~\mathrm{Gyr}$, while the present-day effective equation of state parameter is $\omega_0\approx -0.70$, consistent with accelerated expansion. The NEC and DEC remain satisfied, whereas the SEC is violated at late times. Statistical comparison using the AIC and BIC shows that the proposed model describes the observational data with an accuracy comparable to $\Lambda$CDM, while the BIC generally favors the simpler $\Lambda$CDM model because of its lower complexity.