Observational constraints on the cubic parametrization of the deceleration parameter in f(R, T) gravity

In this paper, we consider the cubic parametrization of the deceleration parameter, in f(R, T) theory of gravitation, where R is the Ricci scalar and T is the trace of the energy-momentum tensor of matter for investigating the expansion history of the universe in the context of flat FRW universe. We use H(z) and SNIa from Union 2.1 compilation datasets with 57 and 580 data points, respectively, in order to obtain the best fit values of the model parameters and the Hubble constant. After constructing the model and solving the modified field equations, by using the best fit values of the parameters, we represent the physical and geometrical properties of the model numerically and discuss their evolution in detail. We show that the model starts with an initial singularity and will have a big rip singularity in the near future. We also show that the model of the universe has evolved from an initial matter-dominated period to one in which it is dominated by dark energy which exhibits behaviour of quintessence currently and phantom in the future.