Coherent State Functional Integral in Loop Quantum Cosmology: Alternative Dynamics

TL;DR

This paper develops a path integral formulation for loop quantum cosmology using coherent states, deriving effective Hamiltonians with quantum corrections that reveal potential observable effects in cosmological dynamics.

Contribution

It introduces a coherent state path integral approach with alternative dynamics, deriving effective Hamiltonians and modified Friedmann equations that incorporate quantum corrections and potential phenomenological differences.

Findings

Effective Hamiltonian with higher-order quantum corrections derived

Moyal product naturally appears in non-symmetric case

Modified Friedmann equations retain signatures of alternative dynamics

Abstract

Coherent state functional integral for the minisuperspace model of loop quantum cosmology is studied. By the well-established canonical theory, the transition amplitude in the path integral representation of loop quantum cosmology with alternative dynamics can be formulated through group averaging. The effective action and Hamiltonian with higher-order quantum corrections are thus obtained. It turns out that for a non-symmetric Hamiltonian constraint operator, the Moyal (star)-product emerges naturally in the effective Hamiltonian. For the corresponding symmetric Hamiltonian operator, the resulted effective theory implies a possible quantum cosmological effect in large scale limit in the alternative dynamical scenario, which coincides with the result in canonical approach. Moreover, the first-order modified Friedmann equation still contains the particular information of alternative dynamics and hence admits the possible phenomenological distinction between the different proposals of quantum dynamics.