Path Integrals and Alternative Effective Dynamics in Loop Quantum Cosmology

TL;DR

This paper explores alternative dynamics in loop quantum cosmology using path integral methods, deriving effective Hamiltonians and modified Friedmann equations that predict quantum bounces consistent with canonical theory.

Contribution

It introduces a path integral formulation for alternative loop quantum cosmology dynamics, showing equivalence of different frameworks and deriving quantum bounce predictions.

Findings

Effective Hamiltonians are equivalent in different frameworks.

First-order modified Friedmann equations predict quantum bounces.

Results align with canonical loop quantum cosmology predictions.

Abstract

The alternative dynamics of loop quantum cosmology is examined by the path integral formulation. We consider the spatially flat FRW models with a massless scalar field, where the alternative quantization inherit more features from full loop quantum gravity. The path integrals can be formulated in both timeless and deparameterized frameworks. It turns out that the effective Hamiltonians derived from the two different viewpoints are equivalent to each other. Moreover, the first-order modified Friedmann equations are derived and predict quantum bounces for contracting universe, which coincide with those obtained in canonical theory.