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Lookup NU author(s): Dr Gerasimos Rigopoulos
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).
The infrared dynamics of a light, minimally coupled scalar field in de Sitter spacetime with Ricci curvature R=12HR=12H, averaged over horizon sized regions of physical volume VH=4π3(1H)3VH=4π3(1H)3, can be interpreted as Brownian motion in a medium with de Sitter temperature TDS=ℏH2πTDS=ℏH2π. We demonstrate this by employing path integral techniques, deriving the effective action of scalar field fluctuations with wavelengths larger than the de Sitter curvature radius and generalizing Starobinsky's seminal results on stochastic inflation. The effective action describes stochastic dynamics and the fluctuating force drives the field to an equilibrium characterized by a thermal Gibbs distribution at temperature TDSTDS which corresponds to a de Sitter invariant state. Hence, approach towards this state can be interpreted as thermalization. We show that the stochastic kinetic energy of the coarse-grained description corresponds to the norm of ∂μϕ∂μϕ and takes a well defined value per horizon volume 12⟨(∇ϕ)2⟩=−12TDS/VH12⟨(∇ϕ)2⟩=−12TDS/VH. This approach allows for the non-perturbative computation of the de Sitter invariant stress energy tensor ⟨Tμν⟩⟨Tμν⟩ for an arbitrary scalar potential. The infrared dynamics of a light, minimally coupled scalar field in de Sitter spacetime with Ricci curvature R=12HR=12H, averaged over horizon sized regions of physical volume VH=4π3(1H)3VH=4π3(1H)3, can be interpreted as Brownian motion in a medium with de Sitter temperature TDS=ℏH2πTDS=ℏH2π. We demonstrate this by employing path integral techniques, deriving the effective action of scalar field fluctuations with wavelengths larger than the de Sitter curvature radius and generalizing Starobinsky's seminal results on stochastic inflation. The effective action describes stochastic dynamics and the fluctuating force drives the field to an equilibrium characterized by a thermal Gibbs distribution at temperature TDSTDS which corresponds to a de Sitter invariant state. Hence, approach towards this state can be interpreted as thermalization. We show that the stochastic kinetic energy of the coarse-grained description corresponds to the norm of ∂μϕ∂μϕ and takes a well defined value per horizon volume 12⟨(∇ϕ)2⟩=−12TDS/VH12⟨(∇ϕ)2⟩=−12TDS/VH. This approach allows for the non-perturbative computation of the de Sitter invariant stress energy tensor ⟨Tμν⟩⟨Tμν⟩ for an arbitrary scalar potential.
Author(s): Rigopoulos G
Publication type: Article
Publication status: Published
Journal: Journal of Cosmology and Astroparticle Physics
Year: 2016
Volume: 2016
Issue: 07
Online publication date: 21/07/2016
Acceptance date: 05/07/2016
Date deposited: 28/07/2016
ISSN (electronic): 1475-7516
Publisher: Institute of Physics Publishing Ltd.
URL: http://dx.doi.org/10.1088/1475-7516/2016/07/035
DOI: 10.1088/1475-7516/2016/07/035
Notes: JCAP07(2016)035 The paper is also available from the arxiv at http://arxiv.org/abs/1604.04313
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