The exact solutions of the field equations with respect to hypersurface-homogeneous Universe filled with perfect fluid in the framework of $f (R, T)$ theory of gravity (Harko et al, \emph{Phys. Rev.} D 84, 024020 (2011)) is derived. The physical behaviour of the cosmological model is studied.

In this paper, we have studied the solutions of plane-symmetric Universe with variable $\omega$ in the presence and the absence of magnetic field of energy density $\rho B$. A special law of variation for Hubble’s parameterproposed by Bermann in {\it Nuovo Cimento} B 74, 182 (1983) has been utilized to solve the field equations. Some physical and kinematical properties of the models are also discussed.

In this paper,we study themodel of $f (T )$ gravity in the presence of dark matter and modified holographic Ricci dark energy (MHRDE) in locally rotationally symmetric (LRS) Bianchi type-I space–time. To achieve a physically realistic solution of the field equations, we have considered volumetric power and exponential expansion laws. We plot the corresponding cosmological parameters for dark energy components in terms of redshift; thereafter we investigate the accelerated expansion of the Universe. The physical and geometrical parameters of the models are also discussed in detail. The Statefinder diagnostic pair and jerk parameter are analysed to characterise completely different phases of the Universe.

In this article, the perfect fluid is introduced for plane symmetric space–time in the framework of teleparallel gravity using hybrid expansion law (HEL). The behaviour of accelerating Universe is discussed by considering the depiction model of $f (T )$ gravity, i.e. $f (T ) = T ^{\eta}$. The geometrical and physical parameters of the model are studied. An effective equation of state (EoS) has been investigated in the cosmological evolution with perfect fluid. The basic equations of thermodynamics have been deduced and the thermodynamical aspects of the model have been discussed. Thermodynamic temperature and entropy density of the model are also obtained. The statefinder parameters and jerk parameter analysis are discussed for our obtained model to distinguish our model from other dark energy models.