Singularity avoidance in the hybrid quantization of the Gowdy model

Abstract

One of the most remarkable phenomena in Loop Quantum Cosmology is that, at least for homogeneous cosmological models, the Big Bang is replaced with a Big Bounce that connects our universe with a previous branch without passing through a cosmological singularity. The goal of this work is to study the existence of singularities in Loop Quantum Cosmology including inhomogeneities and check whether the behavior obtained in the purely homogeneous setting continues to be valid. With this aim, we focus our attention on the three-torus Gowdy cosmologies with linearly polarized gravitational waves and use effective dynamics to carry out the analysis. For this model, we prove that all the potential cosmological singularities are avoided, generalizing the results about resolution of singularities to this scenario with inhomogeneities. We also demonstrate that, if a bounce in the (Bianchi background) volume occurs, the inhomogeneities increase the value of this volume at the bounce with respect to its counterpart in the homogeneous case.

11 pages, 2 figures. v2: clarifications added in Sec. IV, minor corrections in Sec. III A

References in corpus (23)

• Quantum Nature of the Big Bang: Improved dynamics
• Quantum Nature of the Big Bang
• Quantum Nature of the Big Bang: An Analytical and Numerical Investigation
• Loop quantum cosmology of k=1 FRW models
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Are loop quantum cosmos never singular?
• Loop quantum cosmology and the k = - 1 RW model
• Closed FRW model in Loop Quantum Cosmology
• Anti-deSitter universe dynamics in LQC
• Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations
• Loop Quantization of Vacuum Bianchi I Cosmology
• Physical evolution in Loop Quantum Cosmology: The example of vacuum Bianchi I
• Loop Quantum Cosmology in Bianchi Type I Models: Analytical Investigation
• The behavior of non-linear anisotropies in bouncing Bianchi I models of loop quantum cosmology
• Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization of the Gowdy Model
• Effective Dynamics, Big Bounces and Scaling Symmetry in Bianchi Type I Loop Quantum Cosmology
• Quantum gravitational Kasner transitions in Bianchi-I spacetime
• A Hamiltonian Formulation of the BKL Conjecture
• Hybrid Quantum Cosmology: Combining Loop and Fock Quantizations
• Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
• Matter in inhomogeneous loop quantum cosmology: the Gowdy $T^3$ model
• A quantum gravitational inflationary scenario in Bianchi-I spacetime
• The Big Bang and the Quantum

Cited by in corpus (16)

• Kantowski-Sachs spacetime in loop quantum cosmology: bounds on expansion and shear scalars and the viability of quantization
• On effective loop quantum geometry of Schwarzschild interior
• Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime
• The loop quantum cosmology bounce as a Kasner transition
• Hybrid Loop Quantum Cosmology: An Overview
• Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes
• Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes
• Generic absence of strong singularities and geodesic completeness in modified loop quantum cosmologies
• The Martin-Benito-Mena Marugan-Olmedo prescription for the Dapor-Liegener model of Loop Quantum Cosmology
• Modified FRW cosmologies arising from states of the hybrid quantum Gowdy model
• Big Bang Singularity Resolution In Quantum Cosmology
• Hysteresis and beats in loop quantum cosmology
• Quantum mechanics allows setting initial conditions at a cosmological singularity: Gowdy model example
• Modeling effective FRW cosmologies with perfect fluids from states of the hybrid quantum Gowdy model
• Quantum geometric formulation of Brans-Dicke theory for Bianchi I spacetime
• Cosmological dynamics in spin-foam loop quantum cosmology: challenges and prospects