Bianchi type-V perfect fluid space-time models in general relativity

Abstract

The law of variation for the generalized mean Hubble’s parameter in the case of a spatially homogeneous and anisotropic Bianchi type-V space-time metric that yields a constant value of deceleration parameter, is presented. The variation for Hubble’s parameter generates two types of solutions for the average scale factor one is of power-law type and second is of the exponential form. Using these two forms, Einstein’s field equations for perfect fluid Bianchi type-V models are solved separately that correspond to singular and non-singular models respectively. We find that the constant value of deceleration parameter is reasonable for description of the present day universe. We also find that the universe decelerates for positive value of deceleration parameter where as it accelerates for negative one. The behaviors of observationally important parameters such as expansion scalar, mean anisotropic parameter and shear scalar are discussed. Exact expressions for look-back time, luminosity distance and event horizon versus redshift are derived and their significances are discussed in detail. It has been observed that the solutions are compatible with the results of recent observations.