Simple cosmological de Sitter solutions on dS$_4 \times Y_6$ spaces

TL;DR

This paper presents explicit time-dependent solutions to 10D vacuum Einstein equations with compactified six-dimensional warped spaces, demonstrating inflationary de Sitter solutions and highlighting limitations of previous warped models.

Contribution

It provides new explicit 10D solutions with warped internal spaces of various curvatures, advancing understanding of de Sitter compactifications in string theory.

Findings

Found inflationary de Sitter solutions from 10D vacuum Einstein equations.

Showed limitations of previous warped models due to oversimplified metric ansatz.

Provided examples of non-singular warped compactifications on dS$_4$.

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 $S^5$ or an Einstein space $T^{1,1}=(S^2\times S^2)\rtimes S^1$. 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 de Sitter space dS$_4$.