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

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: ${\ensuremath{\mu}}_{0}$ and $\overline{\ensuremath{\mu}}$ in the 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 ${\ensuremath{\mu}}_{0}$ 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 prebounce 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 the $\overline{\ensuremath{\mu}}$ scheme where the emergent matter is a cosmological constant, the emergent matter in the ${\ensuremath{\mu}}_{0}$ scheme behaves as a string gas.