From de Sitter to de Sitter

TL;DR

This paper constructs new higher-dimensional de Sitter supergravity solutions from type IIA* theory, revealing cosmological models with evolving expansion rates and embeddings in string theory.

Contribution

It presents the first explicit construction of de Sitter supergravity solutions from hyperbolic reductions of massive type IIA* theory, including smooth cosmological solutions and their embeddings.

Findings

Constructed D=6, N=(1,1) de Sitter supergravity from type IIA*.

Developed smooth cosmological solutions with evolving expansion rates.

Embedded de Sitter solutions into ten-dimensional string theory.

Abstract

We obtain D=6, N=(1,1) de Sitter supergravity from a hyperbolic reduction of the massive type IIA* theory. We construct a smooth cosmological solution in which the co-moving time runs from an infinite past, which is dS_4\times S^2, to an infinite future, which is a dS_6-type spacetime with the boundary R^3\times S^2. This provides an effective four-dimensional cosmological model with two compact extra dimensions forming an S^2. Interestingly enough, although the solution is time-dependent, it arises from a first-order system via a superpotential construction. We lift the solutions back to D=10, and in particular obtain two smooth embeddings of dS_4 in massive type IIA*, with the internal space being either H^4\times S^2 or an H^4 bundle over S^2. We also obtain the analogous D=5 and D=4 solutions. We show that there exist cosmological solutions that describe an expanding universe with the expansion rate significantly larger in the past than in the future.