An Overview on the Nature of the Bounce in LQC and PQM

Abstract

We present a review on basic aspects of quantum cosmology in the presence of cut-off physics. We first analyze how the Wheeler-DeWitt equation in a pure metric approach describes the quantum Universe, showing how the singularity is not removed. We then discuss basic features of loop quantum cosmology. For the isotropic Universe, we compare the original ${\mu }_0$ scheme and the most commonly accepted formulation, the $\bar{\mu }$ scheme. Some results concerning the Bianchi Universes are also discussed. Finally, we consider some relevant criticisms on the real link between full loop quantum gravity and its minisuperspace implementation. In the second part of the review we consider the isotropic Universe and the Bianchi models in the framework of polymer quantum mechanics. We first address the polymerization in terms of the Ashtekar-Barbero-Immirzi connection and show how the resulting dynamics is isomorphic to the ${\mu }_0$. Then we analyze the polymerization of volume-like variables, and we see the resulting dynamics is isomorphic to the $\bar{\mu }$ scheme with a fixed critical energy density. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model through a metric approach. We compare the results obtained by using the volume variable to the standard Misner variable. In the latter case we find a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations on changing variables in the polymer representation. In particular we consider how the dynamics can be mapped in two different sets of variables (at the price of using a coordinate-dependent lattice step), and we infer some possible implications on the equivalence of the ${\mu }_0$ and $\bar{\mu }$ scheme of loop quantum cosmology.

Review article. Appears in special issue "Quantum Cosmology" of the journal "Universe". 51 pages, 19 figures. See the article for full abstract

References in corpus (36)

• 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
• A Critical Review of Classical Bouncing Cosmologies
• Loop quantum cosmology of k=1 FRW models
• A Short Review of Loop Quantum Gravity
• Corrections to the Friedmann Equations from LQG for a Universe with a Free Scalar Field
• Polymer Quantum Mechanics and its Continuum Limit
• Closed FRW model in Loop Quantum Cosmology
• Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization of the Gowdy Model
• Critical evaluation of common claims in loop quantum cosmology
• Anomaly-free cosmological perturbations in effective canonical quantum gravity
• Consistent Loop Quantum Cosmology
• The Bianchi IX model in Loop Quantum Cosmology
• Quantum suppression of the generic chaotic behavior close to cosmological singularities
• Quantum cosmology from quantum gravity condensates: cosmological variables and lattice-refined dynamics
• The Ups and Downs of Cyclic Universes
• Hamiltonian and physical Hilbert space in polymer quantum mechanics
• Loop Quantum Cosmology of Diagonal Bianchi Type I model: simplifications and scaling problems
• Loop quantum cosmology of a radiation-dominated flat FLRW universe
• Exhaustive investigation of the duration of inflation in effective anisotropic loop quantum cosmology
• Behavior of the Universe anisotropy in a big-bounce cosmology
• Unavoidable shear from quantum fluctuations in contracting cosmologies
• Polymer dynamics of isotropic universe in Ashtekar and in volume variables
• Polymer Quantum Dynamics of the Taub Universe
• Big-bounce cosmology from quantum gravity: The case of a cyclical Bianchi I universe
• Polymer inflation
• Semiclassical and quantum features of the Bianchi I cosmology in the polymer representation
• Semi-Classical Isotropization of the Universe during a de Sitter phase
• Nonsingular cosmology from evolutionary quantum gravity
• Natural Inflation from Polymer Quantization
• Classical and quantum behavior of the generic cosmological solution
• Bianchi I effective dynamics in Quantum Reduced Loop Gravity
• Time evolution in quantum cosmology
• Thermodynamics in new model of loop quantum cosmology
• The Role of Entropy in the Evolutionary Quantization of the Isotropic Universe

Cited by in corpus (28)

• Extended GUP formulation and the role of momentum cut-off
• Comparison of the Semiclassical and Quantum Dynamics of the Bianchi I Cosmology in the Polymer and GUP Extended Paradigms
• Exploring the Hubble tension with a late time Modified Gravity scenario
• Obviating PBH overproduction for SIGWs generated by Pulsar Timing Arrays in loop corrected EFT of bounce
• Emergent Universe Model from Modified Heisenberg Algebra
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Is Bianchi I a Bouncing Cosmology in the Wheeler-DeWitt picture?
• Non-Singular Gravitational Collapse through Modified Heisenberg Algebra
• Semiclassical and quantum features of the Bianchi I cosmology in the polymer representation
• n-dimensional non-commutative GUP quantization and application to the Bianchi I model
• Quantum Big Bounce of the isotropic Universe via a relational time
• Negative non-Gaussianity as a salvager for PBHs with PTAs in bounce
• Dynamics of the Mixmaster Universe in a non-commutative Generalized Uncertainty Principle framework
• On the emergence of a classical Isotropic Universe from a Quantum $f(R)$ Bianchi Cosmology in the Jordan Frame
• A Bouncing Cosmology from VECROs
• Fate of Mixmaster Chaos in a Deformed Algebra framework
• The role of spatial curvature in constraining the Universe anisotropies across a Big Bounce
• Tunnelling-induced cosmic bounce in the presence of anisotropies
• Radiation-dominated bouncing model with slow contraction and inflation
• Is the BKL map an intrinsic feature of the Quantum Mixmaster Universe?
• Quantum Big-Bounce as a phenomenology of RQM in the Mini-superspace
• Quantum geometric formulation of Brans-Dicke theory for Bianchi I spacetime
• Universe bouncing its way to inflation
• Big-Bounce in Quantum f(R)-Cosmology: Polymer Dynamics with Internal Time
• Quantum Isotropic Universe in RQM Analogy: the Cosmological Horizon
• Quantum Gravity Corrections to the inflationary spectrum in a Bohmian approach
• Arrows of time in bouncing cosmologies
• The phenomenology of Quantum Bounce in the Klein-Gordon, Wheeler-DeWitt and Dirac formalisms