Quantum reduced loop gravity effective Hamiltonians from a statistical regularization scheme

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.

arXiv comment22 pages, 4 figures. Two small typos fixed. Conclusions unchanged

References in corpus (32)

• Background Independent Quantum Gravity: A Status Report
• Loop Quantum Cosmology: A Status Report
• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Geometry and Black Hole Entropy
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• A new spinfoam vertex for quantum gravity
• Loop quantum cosmology of k=1 FRW models
• Loop quantum cosmology of Bianchi I models
• Quantum gravity, shadow states, and quantum mechanics
• The pre-inflationary dynamics of loop quantum cosmology: Confronting quantum gravity with observations
• Flipped spinfoam vertex and loop gravity
• Gauge Field Theory Coherent States (GCS) : I. General Properties
• An Extension of the Quantum Theory of Cosmological Perturbations to the Planck Era
• Polymer Quantum Mechanics and its Continuum Limit
• Loop quantum cosmology of Bianchi type IX models
• From black holes to white holes: a quantum gravitational, symmetric bounce
• Loop quantum cosmology of Bianchi type II models
• Complexifier Coherent States for Quantum General Relativity
• Complementarity of representations in quantum mechanics
• Loop quantum cosmology: From pre-inflationary dynamics to observations
• Quantum-Reduced Loop Gravity: Cosmology
• Consistent Loop Quantum Cosmology
• A new perspective on cosmology in Loop Quantum Gravity
• Cosmological singularity resolution from quantum gravity: the emergent-bouncing universe
• Quantum Reduced Loop Gravity: Semiclassical limit
• Quantum Reduced Loop Gravity and the foundation of Loop Quantum Cosmology
• Quantum Reduced Loop Gravity: a realistic Universe
• A quantum reduction to Bianchi I models in loop quantum gravity
• Loop Quantum Cosmology: A brief review
• Quantum-Reduced Loop-Gravity: Relation with the Full Theory
• Improved regularization from Quantum Reduced Loop Gravity
• Cyclic universe from Loop Quantum Gravity

Cited by in corpus (15)

• Spherically symmetric loop quantum gravity: analysis of improved dynamics
• Quantum gravity predictions for black hole interior geometry
• Primordial power spectrum from the Dapor-Liegener model of loop quantum cosmology
• Quantum evolution of black hole initial data sets: Foundations
• Asymptotically de Sitter Universe inside a Schwarzschild black hole
• First-Order Quantum Correction in Coherent State Expectation Value of Loop-Quantum-Gravity Hamiltonian
• Phenomenology of Quantum Reduced Loop Gravity in the isotropic cosmological sector
• Report on session QG3 of the 15th Marcel Grossmann Meeting
• Power spectrum of primordial perturbations for an emergent universe in quantum reduced loop gravity
• Operators of quantum-reduced loop gravity from the perspective of full loop quantum gravity
• Bianchi I effective dynamics in Quantum Reduced Loop Gravity
• Critical Insight into the Cosmological Sector of Loop Quantum Gravity
• Cosmological states in loop quantum gravity on homogeneous graphs
• Master constraint approach to quantum-reduced loop gravity
• On the Role of Fiducial Structures in Minisuperspace Reduction and Quantum Fluctuations in LQC