Exploring the universe expansion history with f(R,T) gravity: Constraints on cosmological parameters

This work examines the cosmological implications of two functional forms of f ( R , T ) = R + α T n gravity: for two different value of n where n = 1 and n ≠ 1, and α and n are free parameters. The modified Friedmann equations are derived, and the cosmic evolution of the Hubble parameter H ( z ) is determined. Cosmological parameters are estimated through χ 2 minimization and MCMC analysis using the emcee algorithm, with model parameters constrained by various observational datasets. Both models reproduce late-time acceleration and remain observationally indistinguishable from ΛCDM, while allowing small deviations parameterized by α and n . The cosmological behavior of the deceleration parameter q ( z ), the jerk, the snap parameter s ( z ), and the effective equation of state parameter ω is also analyzed. The results indicate that the Universe transitioned from deceleration to late-time accelerated expansion, consistent with the ΛCDM model. Analysis of the energy conditions reveals that the NEC and DEC are satisfied, while the SEC is violated, which explains the transition from a decelerating matter-dominated epoch to the present accelerated phase. These findings indicate that the proposed f ( R, T ) models are compatible with current observational data and provide a viable alternative to ΛCDM in describing cosmic acceleration.