Thermal Interpretation of Infrared Dynamics in de Sitter

Abstract

The infrared dynamics of a light, minimally coupled scalar field in de Sitter spacetime with Ricci curvature $R=12H$, averaged over horizon sized regions of physical volume $V_H=\frac{4\pi }{3}{\left(\frac{1}{H}\right)}^3$, can be interpreted as Brownian motion in a medium with de Sitter temperature $T_{DS}=\frac{\hslash H}{2\pi }$. We demonstrate this by directly 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 $T_{DS}$ 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 ${\partial }_{\mu }\varphi$ and takes a well defined value per horizon volume $\frac{1}{2}⟨{\left(\nabla \varphi \right)}^2⟩=-\frac{1}{2}{T}_{DS}/V_H$. This approach allows for the non-perturbative computation of the de Sitter invariant stress energy tensor $⟨T_{\mu \nu }⟩$ for an arbitrary scalar potential.

8 pages, no figures; v2: 9 pages, no figures, some further explanation on the decomposition into long and short wavelengths added. Matches version published in JCAP

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• Probing the Neutrino Mass Hierarchy beyond $\Lambda$CDM Model
• Renormalisation group improvement in the stochastic formalism
• Quantum Effects of Mass on Scalar Field Correlations and Fluctuations during Inflation
• Unequal time correlators of stochastic scalar fields in de Sitter space
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• Fluctuation-dissipation in accelerated frames
• Conformal Vacuum and Fluctuation-Dissipation in de-Sitter Universe and Black Hole Spacetimes
• Free scalar correlators in de Sitter via the stochastic approach beyond slow roll
• Novel mechanism for CMB modulation in the Standard Model
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• Emergent particles of de Sitter: thermal interpretation of the stochastic formalism and beyond