In this paper we discuss the variation law for Hubble's parameter with average scale factor in a spatially homogeneous and anisotropic Bianchi type-V space-time model, which yields constant value of the deceleration parameter. We derive two laws of variation of the average scale factor with cosmic time, one is of power-law type and the other is of exponential form. Exact solutions of Einstein field equations with perfect fluid and heat conduction are obtained for Bianchi type-V space-time in these two types of cosmologies. In the cosmology with the power-law, the solutions correspond to a cosmological model which starts expanding from the singular state with positive deceleration parameter. In the case of exponential cosmology, we present an accelerating non-singular model of the Universe. We find that the constant value of deceleration parameter is reasonable for the present day Universe and gives an appropriate description of evolution of Universe. We have also discussed different types of physical and kinematical behaviour of the models in these two types of cosmologies.

A class of non-singular bouncing cosmological models of a general class of Bianchi models filled with perfect fluid in the framework of $f (R, T)$ gravity is presented. The model initially accelerates for a certain period of time and decelerates thereafter. The physical behaviour of the model is also studied.

The present study deals with hypersurface-homogeneous cosmological models with anisotropic dark energy in Saez–Ballester theory of gravitation. Exact solutions of field equations are obtained by applying a special law of variation of Hubble’s parameter that yields a constant negative value of the deceleration parameter. Three physically viable cosmological models of the Universe are presented for the values of parameter $K$ occurring in the metric of the space–time. The model for $K = 0$ corresponds to an accelerating Universe with isotropic dark energy. The other two models for $K = 1$ and $−1$ represent accelerating Universe with anisotropic dark energy, which isotropize for large time. The physical and geometric behaviours of the models are also discussed.