Self-stabilization of extra dimensions

TL;DR

This paper demonstrates that high-order curvature invariants in gravity theories can stabilize extra dimensions in Kaluza-Klein cosmology, leading to stable small-size extra dimensions and a partial alleviation of the cosmological constant problem.

Contribution

It introduces a general method using high-order curvature invariants for stabilizing extra dimensions in Kaluza-Klein models, applicable to various gravitational actions.

Findings

Stable small extra dimensions achieved in models with quadratic and cubic curvature terms.

Effective scalar potentials with positive minima found, indicating stability.

The approach partially addresses the cosmological constant problem.

Abstract

We show that the problem of stabilization of extra dimensions in Kaluza-Klein type cosmology may be solved in a theory of gravity involving high-order curvature invariants. The method suggested (employing a slow-change approximation) can work with rather a general form of the gravitational action. As examples, we consider pure gravity with Lagrangians quadratic and cubic in the scalar curvature and some more complex ones in a simple Kaluza-Klein framework. After a transition to the 4D Einstein conformal frame, this results in effective scalar field theories with certain effective potentials, which in many cases possess positive minima providing stable small-size extra dimensions. Estimates made in the original (Jordan) conformal frame show that the problem of a small value of the cosmological constant in the present Universe is softened in this framework but is not solved completely.}