Loop quantum cosmology in 2+1 dimension

TL;DR

This paper extends loop quantum cosmology to 2+1 dimensions, demonstrating that the classical big bang singularity is replaced by a quantum bounce, similar to the 3+1 dimensional case, and discusses the differences.

Contribution

It introduces the first isotropic loop quantum cosmology model in 2+1 dimensions and compares it with the 3+1 dimensional model.

Findings

Classical singularity replaced by quantum bounce in 2+1D model

Similarities between 2+1D and 3+1D models in quantum behavior

Differences in the structure of the models

Abstract

As a first step to generalize the structure of loop quantum cosmology to the theories with the spacetime dimension other than four, the isotropic model of loop quantum cosmology in 2+1 dimension is studied in this paper. We find that the classical big bang singularity is again replaced by a quantum bounce in the model. The similarities and differences between the 2+1 dimensional model and the 3+1 dimensional one are also discussed.