The Background Field Approximation in (quantum) cosmology

Abstract

We analyze the Hamilton-Jacobi action of gravity and matter in the limit where gravity is treated at the background field approximation. The motivation is to clarify when and how the solutions of the Wheeler-DeWitt equation lead to the Schrödinger equation in a given background. To this end, we determine when and how the total action, solution of the constraint equations of General Relativity, leads to the HJ action for matter in a given background. This is achieved by comparing two neighboring solutions differing slightly in their matter energy content. To first order in the change of the 3-geometries, the change of the gravitational action equals the integral of the matter energy evaluated in the background geometry. Higher order terms are governed by the ``susceptibility'' of the geometry. These classical properties also apply to quantum cosmology since the conditions which legitimize the use of WKB gravitational waves are concomitant with those governing the validity of the background field approximation.

26 pages, latex, no figures

References in corpus (6)

• Wheeler-DeWitt equation and Feynman diagrams
• Particle creation and non-adiabatic transitions in quantum cosmology
• The interpretation of the solutions of the Wheeler De Witt equation
• Unitary and non-unitary evolution in quantum cosmology
• Gravitational Instanton for Black Hole Radiation
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Cited by in corpus (7)

• Emergent Semiclassical Time in Quantum Gravity. I. Mechanical Models
• Observations in Quantum Cosmology
• Relational Particle Models. II. Use as toy models for quantum geometrodynamics
• Emergent Semiclassical Time in Quantum Gravity. Full Geometrodynamics and Minisuperspace Examples
• On the Semiclassical Approach to Quantum Cosmology
• Gauge Fixing and the Semiclassical Interpretation of Quantum Cosmology
• Semiclassical momentum representation in quantum cosmology