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

Anirudh Pradhan, Gopikant Goswami, Rita Rani, Aroonkumar Beesham

Published 2022-10-26Version 1

We attempt to model a present time accelerating universe, in the framework of FLRW space-time using field equations of f(R,T) gravity and taking $f(R,T) = R + 2 \lambda T$, $\lambda$ being an arbitrary constant. For this, terms containing $\lambda$ in the field equation are assumed as a source of energy producing negative pressure. Our model is a novel one in the sense that the $\lambda$ parameter develops a fluid whose equation of state is parameterized. The model parameters, present values of density, Hubble and deceleration parameters are estimated statistically to arrive at physically viable cosmology. We consider three types of observational data set: $46$ Hubble parameter data set, SNe Ia $715$ data sets of distance modulus and apparent magnitude and 66 Pantheon data set (the latest compilation of SN Ia 40 bined plus 26 high redshift apparent magnitude $m_b$ data set in the redshift range $0.014 \leq z \leq 2.26 $. These data are compared with theoretical results through the $ \chi^2 $ statistical test. The universe model exhibits phase transition from decelerating to accelerating one. We have calculated transional red shifts and time for the data sets. Our estimated results for the present values of various model parameters such Hubble , deceleration etc. are found as per expectations and surveys. We get a very interesting result from estimations that at present, the value of density $\rho_0$ is $\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 present density is attributed to the presence of dark matter and dark energy in the universe. We have also examined the behaviour of pressure in our model. It is negative and is dominant over density $\simeq - 0.7 \rho_0$.