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

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.

Quantisation ambiguities and the effective dynamics of scalar-tensor theories in loop quantum cosmology

“…where we have reset N = 1. The effective Friedmann equation, Klein-Gordon equation and Raychadhuri equation are given by [47],…”

“…Based on this belief, the connection dynamics of STT is formulated in the Jordan frame in [40,41]. The LQC of some specific models of STT are subsequently studied in the Jordan frame in [42][43][44][45], however, the effective equations derived in these references are incomplete, this crucial fact has been pointed out in [46,47] and the complete equations of motion are given there. The implications of the effective equations of motion will be discussed in the current paper.…”

Loop quantum cosmology from an alternative Hamiltonian. II. Including the Lorentzian term

“…The interior of Schwarzschild black holes is also quantized by applying LQC techniques, leading to the singularity resolution [53,[61][62][63] and black hole remnant [64]. Moreover, the LQC framework is also extended to the cosmological models of scalar-tensor theories of gravity [65][66][67][68][69]. All these achievements are related to the implementation of quantum dynamics in the symmetry-reduced models, inheriting from the full LQG.…”