Photon propagator for inflation in the general covariant gauge

Silvije Domazet; Dražen Glavan; Tomislav Prokopec

doi:10.1007/JHEP07(2024)103

Photon propagator for inflation in the general covariant gauge

Silvije Domazet, Dražen Glavan^*, Tomislav Prokopec

^*Corresponding author for this work

Czech Academy of Sciences

Research output: Contribution to journal › Article › Academic › peer-review

Abstract

Photon propagator for power-law inflation is considered in the general covariant gauges within the canonical quantization formalism. Photon mode functions in covariant gauges are considerably more complicated than their scalar counterparts, except for the special choice of the gauge-fixing parameter we call the simple covariant gauge. We explicitly construct the position space photon propagator in the simple covariant gauge, and find the result considerably more complicated than its scalar counterpart. This is because of the need for explicitly inverting the Laplace operator acting on the scalar propagator, which results in Appell’s fourth function. Our propagator correctly reproduces the de Sitter and flat space limits. We use this propagator to compute two simple observables: the off-coincident field strength-field strength correlator and the energy-momentum tensor, both of which yield consistent results. As a spinoff of our computation we also give the exact expression for the Coulomb gauge propagator in power-law inflation in arbitrary dimensions.

Original language	English
Article number	103
Journal	Journal of High Energy Physics
Volume	2024
Issue number	7
DOIs	https://doi.org/10.1007/JHEP07(2024)103
Publication status	Published - Jul 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.

Funding

We are grateful to Richard P. Woodard for explaining to us the origins of conformal anomaly in dimensional regularization; to Igor Khavkine for helpful discussions about the analytic structure of Appell's functions; and to Jose L. Lopez for looking into asymptotic expansions of Appell's first function and sending us preliminary results. DG was supported by the European Union and the Czech Ministry of Education, Youth and Sports (Project: MSCA Fellowship CZ FZU I - CZ.02.01.01/00/22_010/0002906). This work is part of the Delta ITP consortium, a program of the Netherlands Organisation for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW) - NWO project number 24.001.027.

Funders	Funder number
Nederlandse Organisatie voor Wetenschappelijk Onderzoek
European Commission
Ministerstvo Školství, Mládeže a Tělovýchovy
Delta
H2020 Marie Skłodowska-Curie Actions	CZ FZU I — CZ.02.01.01/00/22_010/0002906
Ministerie van onderwijs, cultuur en wetenschap	24.001.027

Keywords

de Sitter space
Gauge Symmetry
Non-Equilibrium Field Theory

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10.1007/JHEP07(2024)103Licence: CC BY

JHEP07(2024)103Final published version, 1.03 MBLicence: CC BY

Cite this

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AB - Photon propagator for power-law inflation is considered in the general covariant gauges within the canonical quantization formalism. Photon mode functions in covariant gauges are considerably more complicated than their scalar counterparts, except for the special choice of the gauge-fixing parameter we call the simple covariant gauge. We explicitly construct the position space photon propagator in the simple covariant gauge, and find the result considerably more complicated than its scalar counterpart. This is because of the need for explicitly inverting the Laplace operator acting on the scalar propagator, which results in Appell’s fourth function. Our propagator correctly reproduces the de Sitter and flat space limits. We use this propagator to compute two simple observables: the off-coincident field strength-field strength correlator and the energy-momentum tensor, both of which yield consistent results. As a spinoff of our computation we also give the exact expression for the Coulomb gauge propagator in power-law inflation in arbitrary dimensions.

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Photon propagator for inflation in the general covariant gauge

Abstract

Bibliographical note

Funding

Keywords

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