Reconstruction of an Observationally Constrained $f(R, T)$ gravity model

In this paper, an attempt is made to construct a Friedmann-Lemaitre-Robertson-Walker model in $f(R,T)$ gravity with a perfect fluid that yields acceleration at late times. We take $f(R,T)$ as $R$ + $8\pi \mu T$. As in the $\Lambda$CDM model, we take the matter to consist of two components, viz., $\Omega_m$ and $\Omega_{\mu}$ such that $\Omega_m$ + $\Omega_{\mu}$=1. The parameter $\Omega_m$ is the matter density (baryons + dark matter), and $\Omega_{\mu}$ is the density associated with the Ricci scalar $R$ and the trace $T$ of the energy momentum tensor, which we shall call dominant matter. We find that at present $\Omega_{\mu}$ is dominant over $\Omega_m$, and that the two are in the ratio 3:1 to 3:2 according to the three data sets: (i) 77 Hubble OHD data set (ii) 580 SNIa supernova distance modulus data set and (iii) 66 pantheon SNIa data which include high red shift data in the range $0\leq z\leq 2.36$. We have also calculated the pressures and densities associated with the two matter densities, viz., $p_{\mu}$, $\rho_{\mu}$, $p_m$ and $\rho_m$, respectively. It is also found that at present, $\rho_{\mu}$ is greater than $\rho_m$. The negative dominant matter pressure $p_{\mu}$ creates acceleration in the universe. Our deceleration and snap parameters show a change from negative to positive, whereas the jerk parameter is always positive. This means that the universe is at present accelerating and in the past it was decelerating. State finder diagnostics indicate that our model is at present a dark energy quintessence model. The various other physical and geometric properties of the model are also discussed.