Extra Dimensions and Inflation

TL;DR

This paper explores a model where extra dimensions evolve during inflation from the electroweak scale, achieving stabilization and appropriate density contrast without supersymmetry or specific potentials.

Contribution

It demonstrates the possibility of inflating and stabilizing extra dimensions from the electroweak scale without supersymmetry, and shows density contrast can be achieved without specific potentials.

Findings

Successful inflation of extra dimensions from electroweak scale to 1 mm

Stabilization of extra dimensions during inflation

Density contrast depends on number of extra dimensions and potential amplitude

Abstract

It has been proposed that, without invoking supersymmetry, it is possible to solve the hierarchy problem provided the fundamental scale in the higher dimensional theory is at a much lower scale than the Planck scale. In this paper we consider a toy model where we allow $4+d$ dimensions to evolve from a region determined by the new fundamental scale, which is in our case is electro-weak scale. We further investigate whether it is possible to inflate not only the 3 uncompactified dimensions but also the extra dimensions. We require around 70 e-foldings to stabilize the size of two extra dimensions from $M_{\rm EW}^{-1}$ to the required 1 mm size. This can be easily achieved during inflation, but once inflation ends their evolution is governed by the dynamical history of the universe in a similar way that of Brans-Dicke field in generalized Einstein theories. We also show that we achieve the right level of density contrast without invoking any specific potential. The density contrast depends on the number of extra dimensions and upon the amplitude of the potential.