QFT in Curved Spacetime from Quantum Gravity: proper WKB decomposition of the gravitational component

Abstract

Starting from a re-analysis of previous work, we construct the proper low energy quantum field theory (QFT) limit of a full quantum gravity theory in the Born-Oppenheimer approach. We separate the gravitational sector into a classical background, given by a vacuum diagonal Bianchi I cosmology, and its quantum perturbations represented by the two graviton degrees of freedom; we further include quantum matter in the form of a test scalar field. We then implement a Born-Oppenheimer separation, where the gravitons and matter play the role of "slow" and "fast" quantum components respectively, and perform a Wentzel-Kramers-Brillouin (WKB) expansion in a Planckian parameter. The functional Schrödinger evolution for matter is recovered after averaging over quantum gravitational effects, provided that a condition is imposed on the gravitons' wave functional. Such a condition fixes the graviton dynamics and is equivalent to the purely gravitational Wheeler-DeWitt constraint imposed in previous approaches. The main accomplishment of the present work is to clarify that QFT in curved spacetime can be recovered in the low energy limit of quantum gravity only after averaging over the graviton degrees of freedom, in the spirit of effective field theory. Furthermore, it justifies a posteriori the implementation of the gravitational Wheeler-DeWitt equation on the "slow" gravitons' wave functional rather than assuming its validity a priori.

8 pages. Title updated and discussion expanded; matches published version

References in corpus (11)

• The Unruh effect and its applications
• Theory of cosmological perturbations in an anisotropic universe
• Quantum-gravitational effects on gauge-invariant scalar and tensor perturbations during inflation: The slow-roll approximation
• Unitarity, clock dependence and quantum recollapse in quantum cosmology
• Unitarity of quantum-gravitational corrections to primordial fluctuations in the Born-Oppenheimer approach
• The Born-Oppenheimer Method, Quantum Gravity and Matter
• WKB Approaches to Restore Time in Quantum Cosmology: Predictions and Shortcomings
• Quantum gravity corrections to the matter dynamics in the presence of a reference fluid
• Lorentz Symmetry in QFT on Quantum Bianchi I Space-Time
• Definition of a time variable with Entropy of a perfect fluid in Canonical Quantum Gravity
• Parametrizing fluids in canonical quantum gravity

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