Cosmology in f (R, T) modified gravity : unified dark matter and dark energy model constrained by current observations

The proposed cosmological model deals with modified Chaplygin gas (MCG) in f(R, T) = R + xi(T) gravity, where R is the Ricci Scalar and T is the trace of energy-momentum tensor. The function xi(T) is chosen as the linear combination of power law and logarithmic form under flat Friedmann-Lemaitre-Robertson-Walker space-time. The model is compatible with current observational data (Pantheon Type Ia Supernova) and confronts the deceleration and state parameters effectively. The model can predict the Big Rip in future infinity and can also tackle the difficulties related to the fine-tuning and the coincidence problem practically. Further, we have numerically solved the modified Friedmann equations in f(R, T) gravity and also performed a Markov Chain Monte Carlo analysis to obtain the best fit parameters of this current cosmological model. These best parameters are then used to compute the cosmographic parameters, i.e., the deceleration parameter, the jerk parameter and the snap parameter. Significantly, the cosmographic test has given valuable insights into the dynamics of the current cosmological model and also enriched us to understand about the cosmic evolution of the accelerated Universe. Additionally, the Statefinder diagnostics and O m diagnostics have provided deeper insights into the dynamics of the cosmic expansion and also provided information to distinguish between both the cosmological frameworks. Furthermore, these tests also reveal that at late times, the current model goes beyond the phantom region. Again, the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) have provided enough support for the current model under consideration, indicating that the present model exhibits a plausible explanation. However, the Lambda CDM model has emerged with the lowest AIC value which suggests its relatively superior fit compared to the current model. Finally, our current model aligns well with several recent observations and unveils various intriguing features about the late time accelerated Universe.