Loop Quantum Cosmology, Modified Gravity and Extra Dimensions

Xiangdong Zhang

doi:10.3390/universe2030015

Abstract

Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures main quantum corrections at the cosmological level. We set up the basic structure of Brans–Dicke (BD) and higher dimensional LQC. The effective dynamical equations of these theories are also obtained, which lay a foundation for the future phenomenological investigations to probe possible quantum gravity effects in cosmology. Some outlooks and future extensions are also discussed.

Highlights

Loop quantum gravity (LQG) is a quantum gravity scheme that tries to quantize general relativity (GR) with the nonperturbative techniques consistently [1,2,3,4]
Many issues of LQG have been carried out in the past thirty years. Among these issues, loop quantum cosmology (LQC), which is the cosmological sector of LQG has received increasing interest and has become one of the most thriving and fruitful directions of LQG [5,6,7,8,9]
In LQC, the classical cosmological singularity is naturally replaced by a quantum bounce [10,11] and avoids the inevitable cosmological singularity in classical GR

Summary

Introduction

Loop quantum gravity (LQG) is a quantum gravity scheme that tries to quantize general relativity (GR) with the nonperturbative techniques consistently [1,2,3,4]. In LQC, the classical cosmological singularity is naturally replaced by a quantum bounce [10,11] and avoids the inevitable cosmological singularity in classical GR This non-perturbatively loop quantization procedure has been successfully generalized to the modified gravity theories such as metric f (R) theories [12,13], Brans–Dicke (BD) theory [14]. The main idea of [38] is that in n + 1 dimensional GR, IJ in order to obtain a well defined connection dynamics, one should adopt SO(n + 1) connections A a rather than the speculated SO(n) connections With these higher dimensional connection dynamics in hand, Thiemann et al successfully generalize the LQG to arbitrary spacetime dimensions.

Classical Connection Dynamics

Quantum Theory

Classical Theory

Effective Equation

Loop Quantum Cosmology in Higher Dimensions

Conclusions