Conformally de Sitter space from anisotropic SD3-brane of type IIB string theory

Abstract

We construct a four dimensional de Sitter space upto a conformal transformation by compactifying the anisotropic SD3-brane solution of type IIB string theory on a six dimensional product space of the form $H_5 \times S^1$, where $H_5$ is a five dimensional hyperbolic space and $S^1$ is a circle. The radius of the hyperbolic space is chosen to be constant. The radius of the circle and the dilaton in four dimensions are time dependent and not constant in general. By different choices of parameters characterizing the SD3-brane solution either the dilaton or the radius of the circle can be made constant but not both. The form-field is also non-vanishing in general, but it can be made to vanish without affecting the solution. This construction might be useful for a better understanding of dS/CFT correspondence as well as for cosmology.