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The thermal backreaction of a scalar field in de Sitter spacetime

Nikos Irges, Antonis Kalogirou, Fotis Koutroulis

TL;DR

This work shows that a light scalar field in de Sitter space experiences explicit curvature-linked thermal effects when the BD vacuum is rotated into a thermal state via Thermo-Field Dynamics. By computing the thermal Wightman function and renormalizing the thermal EMT through point-splitting, the authors derive a finite, conserved $\langle T_{\mu\nu}\rangle_{\beta}$ and analyze its backreaction on the background geometry, finding a deformation of the FRW scale factor whose sign depends on the mass and coupling, and on the initial conditions. The backreaction can either speed up or slow down cosmic expansion, with dominant contributions from superhorizon modes for large $H$, and it is contrasted with the standard $2$-loop graviton corrections. The approach provides a clear, real-time framework to study curvature-thermal effects during inflation and lays groundwork for extensions to more complex field contents and vacua with potential observational consequences through modifications of the power spectrum and slow-roll dynamics.

Abstract

We argue that a scalar field in de Sitter spacetime should feel explicit thermal effects associated with its curvature. Starting from the Bunch-Davies vacuum and a scalar field with small mass compared to the de Sitter curvature, we use the thermo-field dynamics formalism in order to expose these thermal effects. We compute the thermal Wightman function connecting two spacetime points and from it, via the point-splitting regularization technique, the renormalized thermal energy-momentum tensor. We then examine how these corrections affect the de Sitter geometry by solving for the semi-classical backreaction and find that their sign depends on the initial conditions. In order to place our results in context, we compare them to the corresponding 2-loop quantum gravity correction to the cosmological constant derived in [1].

The thermal backreaction of a scalar field in de Sitter spacetime

TL;DR

This work shows that a light scalar field in de Sitter space experiences explicit curvature-linked thermal effects when the BD vacuum is rotated into a thermal state via Thermo-Field Dynamics. By computing the thermal Wightman function and renormalizing the thermal EMT through point-splitting, the authors derive a finite, conserved and analyze its backreaction on the background geometry, finding a deformation of the FRW scale factor whose sign depends on the mass and coupling, and on the initial conditions. The backreaction can either speed up or slow down cosmic expansion, with dominant contributions from superhorizon modes for large , and it is contrasted with the standard -loop graviton corrections. The approach provides a clear, real-time framework to study curvature-thermal effects during inflation and lays groundwork for extensions to more complex field contents and vacua with potential observational consequences through modifications of the power spectrum and slow-roll dynamics.

Abstract

We argue that a scalar field in de Sitter spacetime should feel explicit thermal effects associated with its curvature. Starting from the Bunch-Davies vacuum and a scalar field with small mass compared to the de Sitter curvature, we use the thermo-field dynamics formalism in order to expose these thermal effects. We compute the thermal Wightman function connecting two spacetime points and from it, via the point-splitting regularization technique, the renormalized thermal energy-momentum tensor. We then examine how these corrections affect the de Sitter geometry by solving for the semi-classical backreaction and find that their sign depends on the initial conditions. In order to place our results in context, we compare them to the corresponding 2-loop quantum gravity correction to the cosmological constant derived in [1].

Paper Structure

This paper contains 7 sections, 157 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Definition of the thermal Energy-Momentum Tensor
  3. The renormalized thermal Energy-Momentum Tensor
  4. The thermal backreaction
  5. Conclusions
  6. The renormalized Bunch-Davies Energy-Momentum Tensor
  7. Classical and Bunch-Davies backreactions

Figures (2)

  • Figure 1: The thermal and graviton loop correction for $\xi =0, m^2 = G H^4$. The (orange) line corresponds to the thermal effect while the (blue) curve represents the graviton correction. The square of the logarithm of the latter starts to dominate at late times right after $H \tau_{\rm crit} \simeq -0.547$.
  • Figure 2: The parallel transportation from the points $x_1$ and $x_2$ towards their middle point $x$ using the geodesic tangent vector $t^\mu$.