Exact anisotropic brane cosmologies

Abstract

We present exact solutions of the gravitational field equations in the generalized Randall-Sundrum model for an anisotropic brane with Bianchi type I and V geometry, with perfect fluid and scalar fields as matter sources. Under the assumption of a conformally flat bulk (with a vanishing Weyl tensor) for a cosmological fluid obeying a linear barotropic equation of state the general solution of the field equations can be expressed in an exact parametric form for both Bianchi type I and V space-times. In the limiting case of a stiff cosmological fluid with pressure equal to the energy density, for a Bianchi type I universe the solution of the field equations is obtained in an exact analytic form. Several classes of scalar field models of evolution on the brane are also considered, corresponding to different choices of the scalar field potential. For all models the behavior of the observationally important parameters such as shear, anisotropy, and the deceleration parameter is considered in detail.