Dark energy and cosmic evolution: A study in f(R,T) gravity

In the context of $f(R,T)$ gravity theory for the flat Friedmann-Lemaitre–Robertson–Walker (FLRW) model, the accelerating expansion of the universe is investigated using a specific form of the emergent Hubble parameter. Datasets from $H\left(z\right)$, Type Ia supernovae (SNIa), and Baryon Acoustic Oscillations (BAO) are used to constrain the model and identify the ideal parameter values in order to evaluate the statistical significance of $f(R,T)$ gravity. The best-fit parameters are derived by solving the modified Friedmann equations through a MCMC analysis. These parameters are used to compute the equation of state, statefinders, energy conditions, and the $(\omega -{\omega }^{\prime })$ plane. Furthermore, the evolution of kinematic cosmographic parameters is examined. The findings provide significant behavior and features of dark energy models. Our comprehension of the dynamics and evolution of the universe is improved by this study, which also advances our understanding of dark energy and how it shapes the universe. Also, a key outcome of our study is the demonstration that $f(R,T)$ gravity can account for the Hubble tension through an evolving $H_0$, in agreement with recent findings in modified gravity. Our results provide a significant contribution to the ongoing discussion of modified gravity models and their role in explaining cosmic acceleration, offering an alternative perspective to the standard ΛCDM paradigm.