Stochastic parameters for scalar fields in de Sitter spacetime
File(s)
Published version
Author(s)
Cable, Archie
Rajantie, Arttu
Type
Journal Article
Abstract
The stochastic effective theory approach, often called stochastic inflation, is widely used in cosmology
to describe scalar field dynamics during inflation. The existing formulations are, however, more qualitative
than quantitative because the connection to the underlying quantum field theory (QFT) has not been properly established. A concrete sign of this is that the QFT parameters depend on the renormalization scale, and therefore the relation between the QFT and stochastic theory must have explicit scale dependence that cancels it. In this paper we achieve that by determining the parameters of the second-order stochastic effective theory of light scalar fields in de Sitter to linear order in the self-coupling constant λ. This is done by computing equal-time 2-point correlators to one-loop order both in QFT using dimensional regularization and the MS renormalization scheme and the equal-time 4-point correlator to leading order in both theories, and demanding that the results obtained in the two theories agree. With these parameters,
the effective theory is valid when m ≲ H and λ2 ≪ m4=H4, and therefore it is applicable in cases where neither perturbation theory nor any previously proposed stochastic effective theories are.
to describe scalar field dynamics during inflation. The existing formulations are, however, more qualitative
than quantitative because the connection to the underlying quantum field theory (QFT) has not been properly established. A concrete sign of this is that the QFT parameters depend on the renormalization scale, and therefore the relation between the QFT and stochastic theory must have explicit scale dependence that cancels it. In this paper we achieve that by determining the parameters of the second-order stochastic effective theory of light scalar fields in de Sitter to linear order in the self-coupling constant λ. This is done by computing equal-time 2-point correlators to one-loop order both in QFT using dimensional regularization and the MS renormalization scheme and the equal-time 4-point correlator to leading order in both theories, and demanding that the results obtained in the two theories agree. With these parameters,
the effective theory is valid when m ≲ H and λ2 ≪ m4=H4, and therefore it is applicable in cases where neither perturbation theory nor any previously proposed stochastic effective theories are.
Date Issued
2024-02-15
Date Acceptance
2024-02-01
Citation
Physical Review D, 2024, 109 (4)
ISSN
2470-0010
Publisher
American Physical Society
Journal / Book Title
Physical Review D
Volume
109
Issue
4
Copyright Statement
Published by the American Physical Society Published by the American Physical Society under the terms of the 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.
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Subjects
Astronomy & Astrophysics
CURVED SPACETIME
DISSIPATION
FLATNESS
HORIZON
INFLATIONARY UNIVERSE
Physical Sciences
Physics
Physics, Particles & Fields
QUANTUM-FIELDS
Science & Technology
Publication Status
Published
Article Number
045017
Date Publish Online
2024-02-26