On the Semiclassical Approach to Quantum Cosmology

Abstract

The emergent semiclassical time approach to resolving the problem of time in quantum gravity involves heavy slow degrees of freedom providing via an approximately Hamilton-Jacobi equation an approximate timestandard with respect to which the quantum mechanics of light fast degrees of freedom can run. More concretely, this approach involves Born-Oppenheimer and WKB ansatze and some accompanying approximations. In this paper, I investigate this approach for concrete scaled relational particle mechanics models, i.e. models featuring only relative separations, relative angles and relative times. I consider the heavy-light interaction term in the light quantum equation - necessary for the semiclassical approach to work, firstly as an emergent-time dependent perturbation of the emergent-time-dependent Schrodinger equation for the light subsystem. Secondly, I consider a scheme in which the backreaction is small but non-negligible, so that the l-subsystem also affects the form of the emergent time. I also suggest that the many terms involving expectation values of the light wavefunctions in both the (unapproximated) heavy and light equations might require treatment in parallel to the Hartree--Fock self-consistent approach rather than merely being discarded; for the moment this paper provides a counterexample to such terms being smaller than their unaveraged counterparts. Investigation of these ideas and methods will give us a more robust understanding of the suggested quantum-cosmological origin of microwave background inhomogeneities and galaxies.

20 pages, 1 figure

References in corpus (22)

• Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology
• Inflation model constraints from the Wilkinson Microwave Anisotropy Probe three-year data
• The Problem of Time in Quantum Gravity
• The Problem of Time and Quantum Cosmology in the Relational Particle Mechanics Arena
• Probabilities in Quantum Cosmological Models: A Decoherent Histories Analysis Using a Complex Potential
• Foundations of Relational Particle Dynamics
• New interpretation of variational principles for gauge theories. I. Cyclic coordinate alternative to ADM split
• Triangleland. I. Classical dynamics with exchange of relative angular momentum
• Records Theory
• Geometrodynamics: Spacetime or Space ?
• A comment on "The Cauchy problem of f(R)- gravity", Class. Quantum Grav., 24, 5667 (2007), arXiv:0709.4414
• Triangleland. II. Quantum Mechanics of Pure Shape
• Classical dynamics on triangleland
• Relational mechanics of shape and scale
• Seminar on Records Theory
• Relational Motivation for Conformal Operator Ordering in Quantum Cosmology
• Quantum Cosmological Metroland Model
• Scaled Triangleland Model of Quantum Cosmology
• Shape Quantities for Relational Quadrilateralland
• Geometrodynamics in a spherically symmetric, static crossflow of null dust
• Shape Space Methods for Quantum Cosmological Triangleland
• Quantum Cosmological Relational Model of Shape and Scale in 1-d

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• Minisuperspace model of Machian Resolution of Problem of Time. I. Isotropic Case
• Scaled Triangleland Model of Quantum Cosmology
• Problem of Time: Facets and Machian Strategy
• Quantum Cosmology will need to become a Numerical Subject
• Relational Quadrilateralland. Analogues of Isospin and Hypercharge
• Shape Quantities for Relational Quadrilateralland
• Relational Quadrilateralland Interpretation of CP^2 and Quotients
• Appearances are deceptive: Can graviton have a mass?
• Relational Quadrilateralland. II. The Quantum Theory