Eur. Phys. J. C (2016) 76: 395
https://doi.org/10.1140/epjc/s10052-016-4249-8

Regular Article - Theoretical Physics

Higher dimensional loop quantum cosmology

¹ Department of Physics, South China University of Technology, Guangzhou, 510641, China
² Institute for Quantum Gravity, University of Erlangen-Nürnberg, Staudtstraße 7/B2, 91058, Erlangen, Germany

^* e-mail: xiangdong.zhang@gravity.fau.de

Received: 1 February 2016
Accepted: 5 July 2016
Published online: 13 July 2016

Abstract

Loop quantum cosmology (LQC) is the symmetric sector 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 homogeneous cosmological model in 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 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 dimensional model and the dimensional one. Our model serves as a first example of higher dimensional loop quantum cosmology and offers the possibility to investigate quantum gravity effects in higher dimensional cosmology.