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 $f(R,T) = R + \alpha T^n$ gravity: for two different value of $n$ where $n=1$ and $n\neq 1$, and $\alpha$ 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 $\chi^2$ 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 $\Lambda$CDM, while allowing small deviations parameterized by $\alpha$ 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 $\omega$ is also analyzed. The results indicate that the Universe transitioned from deceleration to late-time accelerated expansion, consistent with the $\Lambda$CDM 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 $\Lambda$CDM in describing cosmic acceleration.