In this work, we study a cosmological model based on the cosmological principle which exhibits a transition from deceleration to acceleration. We consider baryonic matter dark energy (DE), and ‘curvature’ energy. Both baryonic matter and DE have variable equations of state. It is assumed that DE interacts with and transforms energy to baryonic matter. A Friedmann–Robertson–Walker (FRW) Universe filled with two fluids has been discussed. The model is shown to satisfy current observational constraints. This Universe is at present in a phantom phase after passing through a quintessence phase in the past. Various cosmological parameters regarding the accelerating Universe have been presented. The evolution of DE, Hubble, deceleration parameters, etc. have been described with the aid of figures. Our theoretical results have been compared with the SNe Ia related Union 2.1 compilation 581 data and we have observed that our derived model is in good agreement with the current observational constraints. We have also explored the physical properties of the model.

In this paper, we propose that the late-time acceleration of the Universe is due to bulk viscous fluid and trace of energy–momentum tensor $T$ in $f (R, T )$ theory of gravity. We assume that $f (R, T ) = f (R)+2 f (T )$ with $f (R) = R$ and $f (T ) = \lambda T$ where $\lambda$ is a constant, $R$ and $T$ are the Ricci scalar and trace of energy–momentum tensor. First, we obtain an exact solution of the bulk viscous Universe in $f (R, T )$ gravity, then we use observational Hubble data (OHD), the baryon acoustic oscillation (BAO) distance ratio data as well as SN Ia data to constrain the parameters of the derived bulk viscous Universe. Our estimations show that in the model under consideration $H_{0} = 69.089$ km/Mpc/s which is in good agreement with recent astrophysical observations. We ascertain the present age of the derived Universe as well as the signature flipping behaviour of deceleration parameter. Some physical properties of the derived model are also discussed.