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In this paper, a spatially homogeneous and anisotropic Bianchi type V model filled with an imperfect fluid with both viscosity and heat conduction is investigated within the framework of Lyra's geometry. Exact solutions of the field equations are obtained by applying a special law of variation for Hubble's parameter which yields a constant value of the deceleration parameter. Two different physically viable models of the universe are presented in two types of cosmologies, one with power-law expansion and other one with exponential expansion. Cosmological model with power-law expansion has an initial big-bang type singularity at t = 0 whereas the model with exponential expansion has a singularity in the infinite past. The physical and dynamical properties of the models are discussed.

The paper deals with a spatially homogeneous and anisotropic universe filled with perfect fluid and dark energy components. The two sources are assumed to interact minimally together with a special law of variation for the average Hubble's parameter in order to solve the Einstein's field equations. The law yields two explicit forms of the scale factor governing the Bianchi-V spacetime and constant values of deceleration parameter. The role of dark energy with variable equation of state parameter has been studied in detail in the evolution of Bianchi-V universe. It has been found that dark energy dominates the universe at the present epoch, which is consistent with the observations. The universe achieves flatness after the dominance of dark energy. The physical behavior of the universe has been discussed in detail.

A general approach for investigating Bianchi-V cosmological models is introduced in a scalar-tensor theory of gravitation proposed by Saez and Ballester in which the law of variation for Hubble's parameter is taken into account. This variation for Hubble's parameter that yields a constant value of deceleration parameter is then utilized to solve the field equations governing anisotropic Bianchi-V space–time filled with perfect fluid. Two types of exact solutions that correspond to singular and nonsingular models are presented. Finally, we arrive to the conclusion that the universe decelerates for positive value of deceleration parameter whereas it accelerates for negative one. The behaviors of observationally important parameters are discussed in detail. Exact expressions for look-back time, luminosity distance and event horizon versus redshift are derived and their significance are discussed in detail. It has been observed that the solutions are compatible with the results of recent observations.

The field equations within the framework of Lyra's geometry with a time-dependent displacement vector field for a Bianchi type-V space–time filled with a perfect fluid and heat flow are presented. Two different classes of physically viable solutions are obtained by using a special law of variation for the generalized mean Hubble's parameter which correspond to singular and nonsingular models with constant deceleration parameter. These models are found to be consistent with the observations on the present day universe. Some thermodynamical relations are studied. The physical and kinematical behaviors of the models are also discussed.

A special law of variation for Hubble's parameter in anisotropic space–time models that yields a constant value of the deceleration parameter is presented. Also, a spatially homogeneous and anisotropic but locally rotationally symmetric (LRS) Bianchi type-II cosmological model is studied with a perfect fluid and constant deceleration parameter. Assuming the equation of state p = γρ, where 0≤γ≤1, and using a special law of variation for the Hubble parameter, we are able to construct many new solutions to Einstein's field equations of LRS Bianchi type-II for four different physical models (dust, radiation, Zel'dovich and vacuum). We discuss the solutions with power-law and exponential expansion and examine a particular class of models. A detailed study of kinematic, geometrical and observational properties is carried out.