WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings

Abstract

In this review, we analyse different aspects concerning the possibility to separate a gravity-matter system into a part which lives close to a quasi-classical state and a "small" quantum subset. The considered approaches are all relying on a WKB expansion of the dynamics by an order parameter and the natural arena consists of the Bianchi universe minisuperspace. We first discuss how, limiting the WKB expansion to the first order of approximation, it is possible to recover for the quantum subsystem a Schrödinger equation as written on the classical gravitational background. We give some applications for the quantum subsystem in the "corner" configuration of the Bianchi IX model, identifying the quantum variable in the small one of the two anisotropy degrees of freedom. The most surprising result is the possibility to get a non-singular Bianchi IX cosmology when the scenario is extrapolated backwards in time. We also provide some basic hints on the extension of this result to the generic cosmological solution. In the last part of the review, we consider the same scheme to the next order of approximation identifying the quantum subset as made of matter variables only. We deal with the very fundamental problem of non-unitary morphology of the quantum gravity corrections to quantum field theory discussing some proposed reformulations. Instead of constructing the time dependence via that one of the classical gravitational variables on the label time, we analyse a recent proposal to construct time by fixing a reference frame. This scheme can be reached both introducing the so-called "kinematical action", as well as by the well-known Kuchar-Torre formulation. In both cases, the Schrödinger equation, amended for quantum gravity corrections, has the same morphology and we provide a cosmological implementation of the model, to elucidate its possible predictions.

arXiv commentReferences added and discussion expanded. Matches the published version

References in corpus (89)

• The Dynamics of General Relativity
• Resummation of Massive Gravity
• Theoretical Aspects of Massive Gravity
• Massive Gravity in Three Dimensions
• Quantum Nature of the Big Bang
• Dust as a Standard of Space and Time in Canonical Quantum Gravity
• Ghosts in Massive Gravity
• Loop quantum cosmology of Bianchi I models
• Approaches to Quantum Cosmology
• The Schrödinger-Newton equation as non-relativistic limit of self-gravitating Klein-Gordon and Dirac fields
• Reduced Phase Space Quantization and Dirac Observables
• On Unitarity of Massive Gravity in Three Dimensions
• Hilbert Space Structures on the Solution Space of Klein-Gordon Type Evolution Equations
• Conceptual Problems in Quantum Gravity and Quantum Cosmology
• Selection Rules in Minisuperspace Quantum Cosmology
• Quantum Gravity, the Origin of Time and Time's Arrow
• The semiclassical approximation to quantum gravity
• The Born-Oppenheimer Approach to the Matter-Gravity System and Unitarity
• Quantum Mechanics of Klein-Gordon-Type Fields and Quantum Cosmology
• Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The slow-roll approximation
• Wheeler-DeWitt equation and Feynman diagrams
• Classical and Quantum Features of the Mixmaster Singularity
• Massive Gravity Theories and limits of Ghost-free Bigravity models
• A Proposal for Solving the ``Problem of Time" in Canonical Quantum Gravity
• Unitarity, clock dependence and quantum recollapse in quantum cosmology
• Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The de Sitter case
• On the Covariance of the Mixmaster Chaoticity
• On the Generalized Minimal Massive Gravity
• Singularity avoidance in Bianchi I quantum cosmology
• Running the running
• Spike Oscillations
• Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born-Oppenheimer approach
• Does loop quantum cosmology replace the big rip singularity by a non-singular bounce?
• Construction of quantum Dirac observables and the emergence of WKB time
• Self-Adjoint Wheeler-DeWitt Operators, the Problem of Time and the Wave Function of the Universe
• Particle creation and non-adiabatic transitions in quantum cosmology
• Cosmological time and the constants of nature
• Susskind's Challenge to the Hartle-Hawking No-Boundary Proposal and Possible Resolutions
• Classical Inflationary and Ekpyrotic Universes in the No-Boundary Wavefunction
• Inhomogeneous Quantum Mixmaster: from Classical toward Quantum Mechanics
• Cosmological consequences of a principle of finite amplitudes
• Backreaction in Cosmology
• The Born-Oppenheimer Method, Quantum Gravity and Matter
• Frame-independence of the Inhomogeneous Mixmaster Chaos via Misner-Chitre'-like variables
• The Born-Oppenheimer approach to Quantum Cosmology
• Time in quantum cosmology
• The equivalent emergence of time dependence in classical and quantum mechanics
• Semiclassical approximation of the Wheeler-DeWitt equation: arbitrary orders and the question of unitarity
• Minimal Massive 3D Gravity Unitarity Redux
• A Note on the Semi-Classical Approximation in Quantum Gravity
• The picture of the Bianchi I model via gauge fixing in Loop Quantum Gravity
• Dynamical interpretation of the wavefunction of the universe
• Non-Unitarity Problem in Quantum Gravity Corrections to Quantum Field Theory with Born-Oppenheimer Approximation
• On the apparent loss of predictability inside the de-Rham-Gabadadze-Tolley non-linear formulation of massive gravity: The Hawking radiation effect
• Quantum gravity corrections to the matter dynamics in the presence of a reference fluid
• Quantum Cosmology
• Revised Canonical Quantum Gravity via the Frame Fixing
• Renormalizable, asymptotically free gravity without ghosts or tachyons
• Canonical Quantization of Gravity without "Frozen Formalism"
• Minisuperspace Quantum Cosmology in Metric and Affine Theories of Gravity
• Behavior of the Universe anisotropy in a big-bounce cosmology
• Coherent states, quantum gravity and the Born-Oppenheimer approximation, I: General considerations
• Bianchi I model as a prototype for a cyclical Universe
• Dynamics of quantum anisotropies in a Taub Universe in the WKB approximation
• Dualism between Physical Frames and Time in Quantum Gravity
• Probabilistic interpretation of the wave function for the Bianchi I model
• Quantization of the Taub cosmological model with extrinsic time
• Semiclassical suppression of weak anisotropies of a generic Universe
• Quantum Aspects of Massive Gravity II: Non-Pauli-Fierz Theory
• Quantum instability of an oscillating universe
• Quantum Cosmology and the Inflationary Spectra from a Non-Minimally Coupled Inflaton
• The Wavefunction of Anisotropic Inflationary Universes With No-Boundary Conditions
• Definition of a time variable with Entropy of a perfect fluid in Canonical Quantum Gravity
• Quantum dynamics of the corner of the Bianchi IX model in WKB approximation
• Coleman-de Luccia Tunneling Wave Function
• A path-integral approach to the problem of time
• Beyond semiclassical time
• A Scenario for a Singularity-free Generic Cosmological Solution
• Parametrizing fluids in canonical quantum gravity
• Multifractality in the general cosmological solution of Einstein's equations
• The Functional Schrodinger Equation in the Semiclassical Limit of Quantum Gravity with a Gaussian Clock Field
• On the emergence of a classical Isotropic Universe from a Quantum $f(R)$ Bianchi Cosmology in the Jordan Frame
• A Wheeler-DeWitt Equation with Time
• Solution of the noncanonicity puzzle in General Relativity: a new Hamiltonian formulation
• General Relativity as Classical Limit of Evolutionary Quantum Gravity
• Synchronous Quantum Gravity
• Vector Field Induced Chaos in Multi-dimensional Homogeneous Cosmologies
• Concerning Infeasibility of the Wave Functions of the Universe
• WKB approach to the gravity-matter dynamics: a cosmological implementation

Cited by in corpus (16)

• Minisuperspace quantum cosmology in $f(Q)$ gravity
• Study of the Inflationary Spectrum in the Presence of Quantum Gravity Corrections
• QFT in Curved Spacetime from Quantum Gravity: proper WKB decomposition of the gravitational component
• Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group
• A Local Wheeler-DeWitt Measure for the String Landscape
• Generalised Gaussian states in group field theory and $\mathfrak{su}(1,1)$ quantum cosmology
• Analyzing the influence of graviton fluctuations on the inflationary spectrum with a Kuchař-Torre clock
• On the emergence of a classical Isotropic Universe from a Quantum $f(R)$ Bianchi Cosmology in the Jordan Frame
• The role of spatial curvature in constraining the Universe anisotropies across a Big Bounce
• Schrödinger from Wheeler-DeWitt: The Issues of Time and Inner Product in Canonical Quantum Gravity
• Exact path integrals on half-line in quantum cosmology with a fluid clock and aspects of operator ordering ambiguity
• Quantum Mechanics from General Relativity and the Quantum Friedmann Equation
• Quantum Gravity Corrections to the inflationary spectrum in a Bohmian approach
• Quantum Isotropic Universe in RQM Analogy: the Cosmological Horizon
• States of Low Energy on Bianchi I spacetimes
• Dynamics of charged spin-$\frac{1}{2}$ particles in superposed states minimally coupled to electromagnetism in curved spacetime within the WKB approximation