Loop Quantum Kaluza-Klein Cosmology and Inflation

TL;DR

This paper develops a loop quantum Kaluza-Klein cosmology model that naturally resolves classical singularities and achieves sufficient inflation through quantum corrections and extra dimensions.

Contribution

It extends previous models to more general cases, deriving an effective scalar constraint incorporating quantum fluctuations and matter, and demonstrating singularity resolution and inflation.

Findings

Big bang and big rip singularities are resolved by quantum holonomy corrections.

The model achieves over 55 e-folds of inflation after the big bang.

Re-collapse behavior occurs at large scales due to quantum effects.

Abstract

We present the detailed analyses of five-dimensional loop quantum Kaluza-Klein cosmology based on the symmetric reduction of the connection formulation of the full theory. The previous results in a particular scenario are extended to more general cases. The effective scalar constraint for the geometric sector of the model is derived by the systematic semi-classical analysis in both the canonical and path-integral formulations, incorporating the quantum fluctuations as a subleading-order correction. The resulting effective scalar constraint not only exhibits the correct classical limit of the quantum system, but also serves as the basis for investigating the following three distinct effective scenarios through the incorporation of matter contributions: (i) vacuum, (ii) minimally coupling with a scalar field, and (iii) coupling with the dust. In all the three effective scenarios, the big bang and potential past big rip singularities in the classical model are naturally resolved by including the leading-order quantum correction of holonomies. Moreover, the visible universe undergoes a super-inflationary phase after overcoming the classical big bang singularity, during which the phenomenologically desired 55 e-folds can be achieved by appropriate initial conditions. In the case where the subleading-order quantum fluctuation term is included as a constant, the evolutions of the five-dimensional universe in all the three effective scenarios not only achieve sufficient inflation in the visible dimensions, but also exhibit re-collapse behaviors at certain large scales. Hence the cosmic inflation may originate from the interplay between compact extra dimensions and quantum geometric effects.