Investigating the dark energy phenomenon in [formula omitted] cosmological models with observational constraints

Abstract

This paper explores the dark energy phenomenon within the context of f(R,Lm) gravity theory. Two specific non-linear f(R,Lm) models are considered: f(R,Lm)=R2+Lmα and f(R,Lm)=R2+(1+αR)Lm, where the parameter α is free. Here, we adopt a parametrization form for the Hubble parameter in terms of redshift z as H(z)=H0A(1+z)3+B+ϵlog(1+z)12, which allows for deviations from the standard ΛCDM model at both low and high redshifts. We then incorporate the Hubble parameter solution into the Friedmann equations for both models. We employ Bayesian analysis to estimate the constraints on the free parameters H0, A, B, and ϵ using the Hubble measurements and the Pantheon dataset. Further, we investigate the evolution of key cosmological quantities, such as the deceleration parameter, energy density, pressure, EoS parameter, and energy conditions. The evolution of the deceleration parameter reveals a significant transition from a decelerating phase to an accelerating phase in the Universe. The EoS parameter exhibits quintessence-like behavior for both non-linear f(R,Lm) models.