Kaluza-Klein cosmology from five-dimensional Lovelock-Cartan theory

TL;DR

This paper explores how five-dimensional Lovelock-Cartan gravity reduces to four-dimensional cosmology, revealing solutions with dynamic extra dimensions and various universe evolutions.

Contribution

It provides the first detailed analysis of Kaluza-Klein reduction of Lovelock-Cartan theory with explicit cosmological solutions including torsion effects.

Findings

Existence of expanding, contracting, and bouncing universe solutions.

Dynamical compactification of the extra dimension in certain parameter regimes.

Induction of a nonvanishing energy-momentum tensor from torsion and reduced fields.

Abstract

We study the Kaluza-Klein dimensional reduction of the Lovelock-Cartan theory in five-dimensional spacetime, with a compact dimension of $S^1$ topology. We find cosmological solutions of the Friedmann-Robertson-Walker class in the reduced spacetime. The torsion and the fields arising from the dimensional reduction induce a nonvanishing energy-momentum tensor in four dimensions. We find solutions describing expanding, contracting and bouncing universes. The model shows a dynamical compactification of the extra dimension in some regions of the parameter space.