Late-time acceleration in extended and unified f(R,Lm,T) gravity with observational data

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Abstract
In this paper, we investigate the late-time acceleration of the universe within the extended [ ] gravity framework, which unifies curvature, matter Lagrangian, and the trace of the energy–momentum tensor in a single gravitational action. Considering the simplest functional form [ ], we adopt a parametric form of the deceleration parameter [ ] to reconstruct the Hubble parameter [ ]. Using Markov Chain Monte Carlo methods with combined observational Hubble data (OHD) and type Ia supernovae (SNe Ia) datasets, we constrain the cosmological parameters [ ], [ ], and [ ], finding [ ], [ ], and [ ]. Our results indicate a current accelerated expansion and a deceleration-to-acceleration transition consistent with observations. The inferred [ ] value lies between Planck 2018 and local SH0ES measurements, suggesting the parametrization may alleviate the Hubble tension. We further explore the impact of coupling parameters [ ] and [ ] on the energy density, pressure, and equation of state parameter [ ], revealing a quintessence-like dark energy behavior without phantom crossing. These findings demonstrate the versatility of the [ ] model in explaining cosmic acceleration and provide a promising alternative to the standard [ ]CDM cosmology.

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