Dilaton Dynamics in (A)dS_5 x S^5

TL;DR

This paper explores the stabilization of extra dimensions in a ten-dimensional supergravity model with (A)dS_5 x S^5 compactification, showing quantum effects can lead to a stable internal space and a transition from de Sitter to anti-de Sitter space.

Contribution

It provides a quantum-corrected effective potential for the internal space radius, demonstrating stabilization and a universe evolution scenario in IIB supergravity.

Findings

Effective potential has a minimum, stabilizing the internal space.

Universe can evolve from dS_5 to AdS_5 after exponential expansion.

Stabilized S^5 radius remains constant during evolution.

Abstract

We investigate a stabilization of extra dimensions in a ten-dimensional Kaluza-Klein theory and IIB supergravity. We assume (A)dS_5 x S^5 compactifcation, and calculate quantum effects to find an effective potential for the radius of internal space. The effective potential has a minimum, and if the universe is created on the top of the potential hill, the universe evolves from dS_5 to AdS_5 after exponential expansion. The internal space S^5 stays to be small and its radius becomes constant. Our model in IIB supergravity contains the 4-form gauge field with classically vacuum expectation value, which is role of ten-dimensional cosmological constant. If the universe evolves into AdS, the five-dimensional Randall & Sundrum setup with stabilized dilaton is obtained from the type IIB supergravity model.