Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Effective Dynamics of Loop Quantum Kaluza-Klein Cosmology

Shengzhi Li, Yongge Ma, Faqiang Yuan, Xiangdong Zhang

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.

Effective Dynamics of Loop Quantum Kaluza-Klein Cosmology

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.

Paper Structure

This paper contains 4 sections, 6 theorems, 78 equations, 2 figures.

Table of Contents

  1. Symmetry Reduction of Connection Variables
  2. Derivation of the expectation values
  3. Solving the Equations of Motion
  4. Observational Constraints on the Model Parameters

Key Result

Theorem A.1

Given the transformation function $\rho_{\alpha}$, $\forall\alpha$, there exists a unique left action $\tilde{\mathcal{L}}:\mathcal{S}\times P\rightarrow P$ on the principal bundle $P$, commuting with the right action of $G$, such that $\tilde{\mathcal{L}}$ induces the original left action $\mathcal

Figures (2)

  • Figure 1: The evolution of the scale factor $a$, with the inset showing an enlarged view of the local region connected by dashed lines.
  • Figure 2: The evolution of the scale factor $b$, with the inset showing an enlarged view of the local region connected by dashed lines.

Theorems & Definitions (6)

  • Theorem A.1
  • Theorem A.2
  • Theorem A.3
  • Corollary A.3.1
  • Theorem A.4
  • Lemma A.5