Curvature-Assisted Dynamical Compactification in a Pre-Inflationary Higher-Dimensional Universe

TL;DR

This paper explores a mechanism where a higher-dimensional universe dynamically evolves into a four-dimensional one through curvature-assisted radion trapping, with implications for pre-inflationary cosmology.

Contribution

It demonstrates a simple 5D model where negative curvature helps trap the radion, enabling dynamical compactification before inflation.

Findings

Negative curvature sustains tracker-like radion evolution.

Radion can be trapped in a compactified vacuum prior to inflation.

The mechanism illustrates a broader dynamical compactification process.

Abstract

We investigate a pre-inflationary dynamical compactification scenario in which a higher-dimensional expanding universe evolves into an effectively four-dimensional one through curvature-assisted modulus trapping. To obtain a calculable semiclassical realization, we consider a simple five-dimensional $S^1$ compactification in a time-dependent open FRW background. Bulk quantum fields generate both the late-time Casimir contribution that stabilizes the radion and the early-time Kaluza-Klein thermal contributions relevant for the cosmological evolution. We show that negative curvature can sustain tracker-like radion evolution, allowing the radion to be trapped in a compactified vacuum before a subsequent four-dimensional inflationary phase dilutes the curvature remnant. While our analysis is performed in a 5D toy model, it illustrates a broader mechanism by which dynamical compactification can arise in a pre-inflationary higher-dimensional cosmology.