Bianchi Type—IX Barotropic Fluid Model with Time-Dependent Displacement Vector in Lyra Geometry

Abstract

Bianchi Type IX barotropic fluid cosmological model in the frame work of Lyra geometry is investigated. To get the deterministic model of the universe, it is assumed that shear () is proportional to expansion (). This leads to , where and are metric potentials and is a constant. To get the results in terms of cosmic time , we have also considered a special case (dust filled universe) and . We find that the model starts with a big bang initially and the displacement vector () is initially large but decreases due to lapse of time. The models and have point-type singularity at and , respectively. The physical and geometrical aspects of the models are also discussed.