Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme

TL;DR

This paper introduces a statistical regularization scheme in Quantum Reduced Loop Gravity that derives effective Hamiltonians for cosmological models, reproduces known LQC schemes, and suggests an emergent-bouncing universe scenario.

Contribution

It presents a novel regularization approach using density matrices in QRLG, connecting it with established LQC schemes and exploring quantum cosmological dynamics.

Findings

Effective Hamiltonians match LQC $ar{}$ scheme at leading order.

Next-to-leading order corrections influence quantum cosmological dynamics.

Numerical results support the emergent-bouncing universe scenario.

Abstract

We introduce a new regularization scheme for Quantum Cosmology in Loop Quantum Gravity (LQG) using the tools of Quantum Reduced Loop Gravity (QRLG). It is obtained considering density matrices for superposition of graphs based on statistical countings of microstates compatible with macroscopic configurations. We call this procedure statistical regularization scheme. In particular, we show how the $\mu_0$ and $\bar{\mu}$ schemes introduced in Loop Quantum Cosmology (LQC) emerge with specific choices of density matrices. Within this new scheme we compute effective Hamiltonians suitable to describe quantum corrected Friedmann and Bianchi I universes and their leading orders coincide with the corresponding effective LQC Hamiltonians in the $\bar{\mu}$ scheme. We compute the next to the leading orders corrections and numerical investigation of the resulting dynamics shows evidence for the emergent-bouncing universe scenario to be a general property of the isotropic sector of QRLG.