Noncommutative Quantum Cosmology for the FLRW model in Unimodular Gravity

TL;DR

This paper develops a quantum cosmology model for the FLRW universe within Unimodular Gravity, incorporating noncommutative geometry to explore quantum effects and inflationary scenarios.

Contribution

It introduces a noncommutative deformation of the minisuperspace variables in Unimodular Gravity's quantum cosmology framework, extending previous classical equivalence to quantum level.

Findings

Demonstrates how noncommutative geometry affects quantum cosmological dynamics.

Provides insights into inflationary scenarios within the noncommutative Unimodular Gravity framework.

Explores potential deviations from classical predictions due to quantum and noncommutative effects.

Abstract

It is well known that classical Unimodular Gravity (UG) is equivalent to General Relativity, but is not clear the equivalence at the quantum level. Here we exhibit, in the UG framework, the Quantum Cosmology (QC) for a Friedmann-Lemaitre-Robertson-Walker (FLRW) universe, considering an inflationary scenario and also introducing a deformation on the commutation relations for the minisuperspace variables (NCC).