Loop quantum cosmological dynamics of scalar-tensor theory in the Jordan frame

TL;DR

This paper explores the loop quantum cosmological dynamics of scalar-tensor theories in the Jordan frame, deriving effective equations and analyzing specific solutions within Brans-Dicke theory, revealing quantum effects that differ from classical predictions.

Contribution

It introduces holonomy-corrected effective equations for scalar-tensor theories in the Jordan frame and classifies solutions within Brans-Dicke theory, highlighting quantum modifications to classical cosmology.

Findings

Effective equations exhibit unique Jordan frame features.

Exact solutions classified into four cases.

Quantum effects alter late-time cosmological behavior.

Abstract

The effective dynamics of scalar-tensor theory (STT) in the Jordan frame is studied in the context of loop quantum cosmology with holonomy corrections. After deriving the effective Hamiltonian from the connection dynamics formulation, we obtain the holonomy-corrected evolution equations of STT on spatially flat Friedmann-Robterson-Walker background, which exhibit some interesting features unique to the Jordan frame of STT. In particular, the linear term of the cosine function appearing in the equations could lead to dynamics much different from the classical theory in the low-energy limit. In the latter part of this paper, we choose a particular model in STT -- the Brans-Dicke theory to specifically illustrate these features. It is found that in Brans-Dicke theory the effective evolution equations can be classified into four different cases. Exact solutions of the Friedmann equation in terms of the internal time are obtained in these cases. Moreover, the solutions in terms of the proper time describing the late time evolution of the Universe are also obtained under certain approximation; in two cases the solutions coincide with the existing solutions in classical Brans-Dicke theory while in the other two cases the solutions do not.