The fate of four dimensions

TL;DR

This paper discusses the instability of our four-dimensional universe in theories with extra dimensions, showing that positive vacuum energy typically leads to decompactification, with implications for string theory and cosmic acceleration.

Contribution

It demonstrates that positive vacuum energy causes decompactification in extra-dimensional theories, providing insights into the stability of our universe and its relation to string theory potentials.

Findings

Positive vacuum energy leads to decompactification.

Decompactification transitions are generic in extra-dimensional models.

Current cosmic acceleration is unlikely due to ongoing decompactification.

Abstract

In gravitational theories with extra dimensions, it is argued that the existence of a positive vacuum energy generically implies catastrophic instability of our four-dimensional world. The most generic instability is a decompactification transition to growth of the extra dimensions, although other equally bad transitions may take place. This follows from simple considerations based on the form of the potential for the size modulus of the extra dimensions, and apparently offers a resolution of the conundrums presented by eternal de Sitter space. This argument is illustrated in the context of string theory with a general discussion of potentials generated by fluxes, wrapped branes, and stringy corrections. Moreover, it is unlikely that the present acceleration of the Universe represents an ongoing transition in a quintessence scenario rolling towards decompactification, unless the higher dimensional theory has a cosmological constant.