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We attempt to construct a Friedmann-Lemaitre-Robertson-Walker(FLRW)cosmological model in $f(R, T)$ gravity which exhibits a phase transition fromdeceleration to acceleration at present. We take $f(R,T) = R + 2 \lambda T$,$\lambda$ being an arbitrary constant. In our model, the $\lambda$ parameterdevelops a negative pressure in the universe whose Equation of state isparameterized. The present values of model parameters such as density, Hubble,deceleration, Equation of state, and $\lambda$ are estimated statistically byusing the Chi-Square test. For this, we have used three different types ofobservational data sets: the $46$ Hubble parameter data set, the SNeIa $715$data sets of distance modulus, and the 66 Pantheon data set (the latestcompilation of SNeIa 40 bined plus 26 high red shift apparent magnitude $m_b$data set in the red shift ranges from $0.014 \leq z \leq 2.26 $). We havecalculated the transitional red shift and time. The estimated results for thepresent values of various model parameters are found as per expectations andsurveys. Interestingly, we get the present value of the density $\rho_0$,$\simeq 1.5 \rho_c $. The critical density is estimated as $\rho_c\simeq 1.88 ~h_0^2~10^{-29}~gm/cm^3 $ in the literature. The higher value of the presentdensity is attributed to the presence of some additional energies in theuniverse apart from baryon energy. We have examined the behavior of thepressure in our model. It is negative and produces acceleration in theuniverse. Its present value is obtained as $p_0 \simeq - 0.7 \rho_0$.

An f(R,T) Gravity Based FLRW Model and Observational Constraints