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Lookup NU author(s): Dr Gerasimos Rigopoulos
This work is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0).
© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. We provide a formulation of stochastic inflation in full general relativity that goes beyond the slow-roll and separate universe approximations. We show how gauge-invariant Langevin source terms can be obtained for the complete set of Einstein equations in their Arnowitt-Deser-Misner formulation by providing a recipe for coarse-graining the spacetime in any small gauge. These stochastic source terms are defined in terms of the only dynamical scalar degree of freedom in single-field inflation and all depend simply on the first two time derivatives of the coarse-graining window function, on the gauge-invariant mode functions that satisfy the Mukhanov-Sasaki evolution equation, and on the slow-roll parameters. It is shown that this reasoning can also be applied to include gravitons as stochastic sources, thus enabling the study of all relevant degrees of freedom of general relativity for inflation. We validate the efficacy of these Langevin dynamics directly using an example in uniform field gauge, obtaining the stochastic e-fold number in the long wavelength limit without the need for a first-passage-time analysis. As well as investigating the most commonly used gauges in cosmological perturbation theory, we also derive stochastic source terms for the coarse-grained Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations, which enables a well-posed implementation for 3+1 numerical relativity simulations.
Author(s): Launay YL, Rigopoulos GI, Shellard EPS
Publication type: Article
Publication status: Published
Journal: Physical Review D
Year: 2024
Volume: 109
Issue: 12
Online publication date: 17/06/2024
Acceptance date: 03/05/2024
Date deposited: 01/07/2024
ISSN (print): 2470-0010
ISSN (electronic): 2470-0029
Publisher: American Physical Society
URL: https://doi.org/10.1103/PhysRevD.109.123523
DOI: 10.1103/PhysRevD.109.123523
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