Bianchi type-V string cosmological models in general relativity are investigated. To get the exact solution of Einstein’s field equations, we have taken some scale transformations used by Camci et al [Astrophys. Space Sci. 275, 391 (2001)]. It is shown that Einstein’s field equations are solvable for any arbitrary cosmic scale function. Solutions for particular forms of cosmic scale functions are also obtained. Some physical and geometrical aspects of the models are discussed.

In the present work, we have searched for the existence of anisotropic and non-singular compact star in the $f (R, T)$ gravity by taking into account the non-exotic equation of state (EoS). In order to obtain the solutions of the matter content of the compact object, we assume the well-known barotropic form of EoS that yields the linear relation between pressures and energy density. We propose the existence of non-exotic compact star which shows the validation of energy conditions and stability within the perspective of $f (R,T)$ extended theory of gravity. The linear material correction in the extended theory and matter content of compact star can remarkably satisfy energy condition. We discuss various physical features of the compact star and show that the proposed model of the stellar object satisfies all regularity conditions and is stable as well as singularity-free.

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.