Accelerating universe from warped extra dimensions

TL;DR

This paper explores how warped extra dimensions can naturally produce a small positive cosmological constant, providing explicit non-singular de Sitter solutions in higher-dimensional gravity theories.

Contribution

It presents explicit non-singular de Sitter solutions in five and ten dimensions, linking the cosmological constant to extra-dimensional and universe expansion scales.

Findings

Derived de Sitter solutions in higher dimensions.

Linked cosmological constant to extra-dimensional and expansion scales.

Demonstrated non-singular, explicit solutions.

Abstract

Accelerating universe or the existence of a small and positive cosmological constant is probably the most pressing obstacle as well as opportunity to significantly improving the models of four-dimensional cosmology from fundamental theories of gravity, including string theory. In seeking to resolve this problem, one naturally wonders if the real world can somehow be interpreted as an inflating de Sitter brane embedded in a higher-dimensional spacetime described by warped geometry. In this scenario, the four-dimensional cosmological constant may be uniquely determined in terms of two length scales: one is a scale associated with the size of extra dimensions and the other is a scale associated with the expansion rate of our universe. In some specific cases, these two scales are complementary to each other. This result is demonstrated here by presenting some explicit and completely non-singular de Sitter space dS$_4$ solutions of vacuum Einstein equations in five and ten dimensions.