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Super-Hubble de Sitter Fluctuations and the Dynamical RG

C. P. Burgess, L. Leblond, R. Holman, S. Shandera

TL;DR

This work addresses the problem of secular growth in de Sitter fluctuations that can undermine perturbation theory. It applies the Dynamical Renormalization Group (DRG) to resum leading infrared logs and reveal a mass-like IR regulation in a massless scalar with quartic self-interaction, yielding an effective dynamical mass M_eff^2 proportional to (λ H^2)/(8π^2) ln(μ L). Across large-N generalizations, DRG results agree with dynamical mass generation and stochastic-inflation arguments, while for a cubic interaction no dynamical mass arises. The study clarifies how DRG connects RG methods, de Sitter quantum field theory, and late-time IR physics, with implications for primordial fluctuations and potential extensions to scenarios with broken de Sitter invariance.

Abstract

Perturbative corrections to correlation functions for interacting theories in de Sitter spacetime often grow secularly with time, due to the properties of fluctuations on super-Hubble scales. This growth can lead to a breakdown of perturbation theory at late times. We argue that Dynamical Renormalization Group (DRG) techniques provide a convenient framework for interpreting and resumming these secularly growing terms. In the case of a massless scalar field in de Sitter with quartic self-interaction, the resummed result is also less singular in the infrared, in precisely the manner expected if a dynamical mass is generated. We compare this improved infrared behavior with large-N expansions when applicable.

Super-Hubble de Sitter Fluctuations and the Dynamical RG

TL;DR

This work addresses the problem of secular growth in de Sitter fluctuations that can undermine perturbation theory. It applies the Dynamical Renormalization Group (DRG) to resum leading infrared logs and reveal a mass-like IR regulation in a massless scalar with quartic self-interaction, yielding an effective dynamical mass M_eff^2 proportional to (λ H^2)/(8π^2) ln(μ L). Across large-N generalizations, DRG results agree with dynamical mass generation and stochastic-inflation arguments, while for a cubic interaction no dynamical mass arises. The study clarifies how DRG connects RG methods, de Sitter quantum field theory, and late-time IR physics, with implications for primordial fluctuations and potential extensions to scenarios with broken de Sitter invariance.

Abstract

Perturbative corrections to correlation functions for interacting theories in de Sitter spacetime often grow secularly with time, due to the properties of fluctuations on super-Hubble scales. This growth can lead to a breakdown of perturbation theory at late times. We argue that Dynamical Renormalization Group (DRG) techniques provide a convenient framework for interpreting and resumming these secularly growing terms. In the case of a massless scalar field in de Sitter with quartic self-interaction, the resummed result is also less singular in the infrared, in precisely the manner expected if a dynamical mass is generated. We compare this improved infrared behavior with large-N expansions when applicable.

Paper Structure

This paper contains 17 sections, 97 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Next-to-Leading Order de Sitter calculations
  3. Scalars in de Sitter space
  4. Divergences
  5. Loop corrections
  6. Large logs and secular time dependence
  7. RG Methods
  8. The standard argument
  9. The dynamical RG
  10. The dynamical RG for de Sitter fluctuations
  11. Comparisons to other results
  12. Massive scalar field
  13. Massive loop calculation
  14. Dynamical mass at large $N$
  15. Scalar field with a cubic interaction
  16. ...and 2 more sections

Figures (2)

  • Figure 1: The one-loop contribution to the $G_{ C}$ propagator. An additional contribution comes from the related diagram with $\tau_1$ and $\tau_2$ exchanged. Solid lines represent $G_{ C}$, dashed-to-solid lines represent $G_{ R}$, and the crossed circle denotes the counterterms.
  • Figure 2: The three contributions to $G_c(k,\tau_1,\tau_2)$ at one loop. Diagram (a) is divergent in the UV and IR, (b) is only IR divergent, and (c) diverges only in the UV.