Loop quantum Brans-Dicke cosmology

TL;DR

This paper applies loop quantum cosmology techniques to Brans-Dicke theory, showing that quantum effects replace the classical big bang singularity with a bounce, and introduces effective equations for phenomenological studies.

Contribution

It extends loop quantum cosmology to Brans-Dicke theory, deriving quantum difference equations and effective dynamics with the scalar field acting as an emergent time.

Findings

Quantum difference equations replace classical evolution equations.

Classical big bang singularity is replaced by a quantum bounce.

Effective equations facilitate phenomenological analysis of quantum gravity effects.

Abstract

The spatially flat and isotropic cosmological model of Brans-Dicke theory with coupling parameter $\omega\neq-3/2$ is quantized by the approach of loop quantum cosmology. An interesting feature of this model is that, although the Brans-Dicke scalar field is non-minimally coupled with curvature, it can still play the role of an emergent time variable. In the quantum theory, the classical differential equation which represents cosmological evolution is replaced by a quantum difference equation. The effective Hamiltonian and modified dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology. The effective equations indicate that the classical big bang singularity is again replaced by a quantum bounce in loop quantum Brans-Dicke cosmology.