Energy conditions and late-time cosmic acceleration from a divergence-free deceleration parameter in f(R,T) gravity with non-minimal coupling

Abstract

In this work, we study a divergence-free parameterization of the deceleration parameter within the simplest linear f(R,T) modified-gravity model featuring a non-minimal matter-geometry coupling, f(R,T)=R+2λT, where R is the Ricci scalar, T is the trace of the energy-momentum tensor, and λ is the coupling parameter. Using this parameterization, we derive the Hubble parameter as a function of redshift, H(z), and substitute it into the modified Friedmann equations. The model parameters are constrained with observational data from OHD (cosmic chronometers) and the Pantheon supernova compilation, and the present-day values of H_0, q_0, and the evolutionary component q_1 are numerically estimated; the results indicate a smooth transition of the Universe from decelerated to accelerated expansion. In addition, for different values of λ, we analyze the time evolution of the energy density ρ and the effective equation-of-state parameter ω, identify deviations from the ΛCDM scenario, and clarify the role of λ in shaping the global cosmological dynamics. The energy-condition analysis shows that the NEC and DEC are satisfied throughout the evolution, whereas the SEC is violated at late times, in agreement with the observed cosmic acceleration. Overall, the divergence-free parameterization within f(R,T) gravity provides a viable framework to account for late-time acceleration while remaining consistent with observational and theoretical constraints. The results also provide a basis for a comparative analysis with the standard ΛCDM model and for placing observational bounds on the coupling parameter λ.