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

TL;DR

The paper presents a brane-world cosmology with sub-millimeter extra dimensions in which inflation occurs while the internal dimensions are still small, driven by the radion or its stabilization potential. It shows that one can obtain $N_e\gtrsim 100$ and COBE-scale density perturbations without invoking ultra-light inflatons, with the perturbation amplitude tied to the inflationary Hubble scale and the initial internal size $b_I$; the internal dimensions then evolve toward stabilization, while our brane undergoes a period of slow contraction. Exact Kasner-like solutions describe the post-inflationary contraction, during which bulk gravitons are suppressed and a Big Bounce reheats the wall via blue-shifted Hawking radiation, leading to expansion and stabilization of the internal space; a radion moduli problem is identified and argued to be solvable with a modest amount of late-time inflation. The framework yields a self-consistent early universe cosmology in higher dimensions, with natural explanations for horizon/flatness/age problems, a near-scale-invariant spectrum, and reheating that remains compatible with normalcy bounds, while highlighting a radion-related challenge that informs future work on late-time cosmology.

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 $δρ/ρ$ 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.