Effective Dynamics of Loop Quantum Kaluza-Klein Cosmology

TL;DR

This paper develops an effective quantum cosmological model in five dimensions that avoids classical singularities, predicts a dynamical compactification of extra dimensions, and explains cosmic inflation and dark energy through quantum effects.

Contribution

It introduces a loop quantum Kaluza-Klein cosmology with a semiclassical effective scalar constraint, revealing singularity avoidance and dynamical compactification.

Findings

Classical singularities replaced by quantum bounces and collapses.

Dynamical compactification of extra dimension achieved.

Three cosmological epochs: super-inflation, deceleration, late-time acceleration.

Abstract

The five-dimensional loop quantum Kaluza-Klein cosmology is constructed based on the symmetric reduction of the connection formulation of the full theory. Through semiclassical analysis, the effective scalar constraint for the cosmological model coupled with a dust field is derived, incorporating the quantum fluctuations of geometry as a subleading order correction. It demonstrates that the quantum model has the correct classical limit. The explicit solutions to the equations of motion show that the big bang and past big rip singularities in the classical model are avoided by a quantum bounce and a quantum collapse respectively in the effective model. In a particular scenario, the dynamical compactification of the extra dimension is realized, while the observable four-dimensional universe transitions through three distinct epochs: (i) a super-inflationary phase generating 55 e-folds, (ii) a decelerated expansion era, and (iii) a late-time accelerated expansion phase driven by quantum fluctuations. These results suggest that both cosmic inflation and dark energy may originate from the interplay between the compact extra dimension and quantum geometric effects.