LRS Bianchi Type II tilted barotropic fluid cosmological model with heat conduction in general relativity

Abstract

A tilted cosmological model is studied for a barotropic fluid distribution with heat conduction in the framework of a compact Bianchi Type II space-time. To get a deterministic solution in terms of cosmic time t, we have used the supplementary condition R = S n between the metric potentials R and S, where n is a constant. The shear tensor σ ij for the tilted model satisfies the trace-free condition σ ij v j = 0, where v i is the fluid velocity vector. In a special case, the model becomes non-tilted. The heat conduction vector q i also satisfies the trace-free condition q i v i = 0. The spatial volume increases as time increases, and the model represents an inflationary scenario. The model for a barotropic fluid distribution represents decelerating and accelerating phases of the universe, matching with the astronomical observations. Anisotropy is maintained throughout, but in a special case the model isotropizes. The particle horizon and entropy are discussed. We have also discussed the stiff fluid case with physical and geometrical aspects of the models.