Rapid Asymmetric Inflation and Early Cosmology in Theories with Sub-Millimeter Dimensions

TL;DR

This paper explores models of inflation within theories featuring sub-millimeter extra dimensions, demonstrating how inflation can occur with the size of these dimensions still small and producing observable density perturbations consistent with COBE data.

Contribution

It introduces models of inflation driven by the moduli of extra dimensions, showing how they can produce sufficient efoldings and scale-invariant perturbations, with a detailed analysis of the post-inflationary contraction phase.

Findings

Inflation can occur while extra dimensions are still small.

Density perturbations match COBE measurements in magnitude and spectrum.

Post-inflation, the universe undergoes contraction with stabilized extra dimensions.

Abstract

It was recently pointed out that the fundamental Planck mass could be close to the TeV scale with the observed weakness of gravity at long distances being due the existence of new sub-millimeter spatial dimensions. In this picture the standard model fields are localized to a $(3+1)$-dimensional wall or ``3-brane''. We show that in such theories there exist attractive models of inflation that occur while the size of the new dimensions are still small. We show that it is easy to produce the required number of efoldings, and further that the density perturbations $\delta\rho/\rho$ as measured by COBE can be easily reproduced, both in overall magnitude and in their approximately scale-invariant spectrum. In the minimal approach, the inflaton field is just the moduli describing the size of the internal dimensions, the role of the inflationary potential being played by the stabilizing potential of the internal space. We show that under quite general conditions, the inflationary era is followed by an epoch of contraction of our world on the brane, while the internal dimensions slowly expand to their stabilization radius. We find a set of exact solutions which describe this behavior, generalizing the well-known Kasner solutions. During this phase, the production of bulk gravitons remains suppressed. The period of contraction is terminated by the blue-shifting of Hawking radiation left on our wall at the end of the inflationary de Sitter phase. The temperature to which this is reheated is consistent with the normalcy bounds. We give a precise definition of the radion moduli problem.