Constraining dark energy equations of state in $F(R,T)$ gravity

In this paper, we examine the acceleration of the Universe's expansion in $F(R,T)$ gravity, where $R$ denotes the Ricci scalar and $T$ the trace of energy-momentum tensor. Indeed, the unknown nature of the source controlling this acceleration in general relativity leads scientists to investigate its properties by means of some alternative theories to general relativity. Our study is restricted to the particular case where $F(R,T)=R+2\kappa^2 \lambda T$ , with $\lambda$ being a constant. We use a Bayesian analysis of current observational datasets, including the type Ia supernovae constitution compilation and $H(z)$ measurements, to constrain free parameters of the model. To parametrize dark energy, we consider two well known equations of state. We find the best fit values for each model by running a Markov chain Monte Carlo technic. The best fit parameters are used to compare both models to $\Lambda$CDM by means of the Akaike information criterion and the Bayesian information criterion. We show that the Universe underwent recently a transition from a deceleration to an acceleration for both models. Furthermore, the data shows a phantom nature of the equation of state for both models.