Higher dimensional Loop Quantum Cosmology

TL;DR

This paper extends loop quantum cosmology to arbitrary spacetime dimensions, showing that quantum effects resolve the big bang singularity via a bounce in higher dimensions, and identifies two distinct quantum sectors.

Contribution

It introduces the first higher-dimensional loop quantum cosmology model, deriving effective dynamics and revealing qualitative differences based on spacetime dimensionality.

Findings

Quantum bounce resolves big bang singularity in all dimensions.

Two distinct quantum sectors emerge depending on spacetime dimension.

Effective Hamiltonian and modified equations are derived for n+1 dimensions.

Abstract

Loop quantum cosmology(LQC) is the symmetric model of loop quantum gravity. In this paper, we generalize the structure of loop quantum cosmology to the theories with arbitrary spacetime dimensions. The isotropic and homogenous cosmological model in n+1 dimensions is quantized by the loop quantization method. Interestingly, we find that the underlying quantum theories are divided into two qualitatively different sectors according to spacetime dimensions. The effective Hamiltonian and modified dynamical equations of n+1 dimensional LQC are obtained. Moreover, our results indicate that the classical big bang singularity is resolved in arbitrary spacetime dimensions by a quantum bounce. We also briefly discuss the similarities and differences between the n+1 dimensional model and the 3+1 dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers possibility to investigate quantum gravity effects in higher dimensional cosmology.