QFT in curved spacetime from quantum gravity: Proper WKB decomposition of the gravitational component

Journal Article · Mon Mar 13 00:00:00 EDT 2023 · Physical Review. D.

DOI:https://doi.org/10.1103/physrevd.107.l061901· OSTI ID:2424702

Maniccia, Giulia ^[1]; Montani, Giovanni ^[2]; Antonini, Stefano ^[3]

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1. University of Rome (Italy)
2. FNS Department (Italy); University of Rome (Italy)
3. University of Maryland, College Park, MD (United States)

Starting from a reanalysis 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 roles of “slow” and “fast” quantum components, respectively, and perform a 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. Here, 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.

• Research Organization: US Department of Energy (USDOE), Washington, DC (United States). Office of Science, Advanced Scientific Computing Research (ASCR)
• Sponsoring Organization: USDOE
• OSTI ID: 2424702
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 6 Vol. 107; ISSN 2470-0010
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

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