Some physical implications of regularization ambiguities in SU(2) gauge-invariant loop quantum cosmology

TL;DR

This paper investigates how regularization choices in gauge-invariant loop quantum cosmology influence singularity resolution, bounce behavior, and the nature of emergent matter, revealing that different schemes lead to qualitatively different physical outcomes.

Contribution

It demonstrates that gauge-covariant fluxes affect singularity resolution and bounce features across regularization schemes, and shows the unviability of the $$-scheme with a positive cosmological constant.

Findings

Gauge-covariant fluxes enable singularity resolution and bounce in Thiemann-regularized dynamics.

The $$-scheme is unviable with a positive cosmological constant.

Emergent matter differs: cosmological constant in $ar $-scheme, string gas in $$-scheme.

Abstract

The way physics of loop quantum gravity is affected by the underlying quantization ambiguities is an open question. We address this issue in the context of loop quantum cosmology using gauge-covariant fluxes. Consequences are explored for two choices of regularization parameters: $\mu_0$ and $\bar \mu$ in presence of a positive cosmological constant, and two choices of regularizations of the Hamiltonian constraint in loop quantum cosmology: the standard and the Thiemann regularization. We show that novel features of singularity resolution and bounce, occurring due to gauge-covariant fluxes, exist also for Thiemann-regularized dynamics. The $\mu_0$-scheme is found to be unviable as in standard loop quantum cosmology when a positive cosmological constant is included. Our investigation brings out a surprising result that the nature of emergent matter in the pre-bounce regime is determined by the choice of regulator in the Thiemann regularization of the scalar constraint whether or not one uses gauge-covaraint fluxes. Unlike $\bar \mu$-scheme where the emergent matter is a cosmological constant, the emergent matter in $\mu_0$-scheme behaves as a string gas.