Simple cosmological de Sitter solutions on spaces

Abstract

Explicit time-dependent solutions of the 10D vacuum Einstein equations are found for which spacetime is compactified on six-dimensional warped spaces. We explicitly work out an example where the internal manifold is a six-dimensional generalized space having positive, negative or zero scalar curvature, whose base can be a five-sphere S5 or an Einstein space T1, 1 = (S2 × S2)⋊S1. In this paper, inflationary de Sitter solutions are found just by solving the 10D vacuum Einstein equations. Our results further show that the limitation with warped models studied to date has arisen partly from an oversimplification of the 10D metric ansatz. We also give some explicit examples of a non-singular warped compactification on the de Sitter space dS4.