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Particle decay in inflationary cosmology

D. Boyanovsky, H. J. de Vega

TL;DR

This work develops a dynamical renormalization group (DRG) framework to define and compute particle decay during inflation in de Sitter space, where energy is not globally conserved. By analyzing a simple trilinear interaction between a massive decaying field and massless conformally coupled products, the authors derive DRG-improved relaxation laws for superhorizon and subhorizon modes, linking the decay rate to de Sitter features and showing enhancement relative to Minkowski space. The results reveal a decay exponent $\Gamma_1$ with $\Gamma_{\mathrm{dS}}=H\,\Gamma_1$ for superhorizon modes, a Hawking-temperature interpretation, and a horizon-crossing scenario where long-wavelength power is suppressed. The findings suggest potentially measurable imprints on the primordial power spectrum and non-Gaussianities, motivating further gauge-invariant analyses of interacting perturbations during inflation.

Abstract

We investigate the relaxation and decay of a particle during inflation by implementing the dynamical renormalization group. This investigation allows us to give a meaningful definition for the decay rate in an expanding universe. As a prelude to a more general scenario, the method is applied here to study the decay of a particle in de Sitter inflation via a trilinear coupling to massless conformally coupled particles, both for wavelengths much larger and much smaller than the Hubble radius. For superhorizon modes we find that the decay is of the form eta^{Gamma1} with eta being conformal time and we give an explicit expression for Gamma1 to leading order in the coupling which has a noteworthy interpretation in terms of the Hawking temperature of de Sitter space-time. We show that if the mass M of the decaying field is << H then the decay rate during inflation is enhanced over the Minkowski spacetime result by a factor 2H/[pi M]. For wavelengths much smaller than the Hubble radius we find that the decay law is e^{-alpha/[k H C(eta)} with C(eta) the scale factor and alpha determined by the strength of the trilinear coupling. This result suggests a suppression of power for long wavelength modes upon horizon crossing. In all cases we find a substantial enhancement in the decay law as compared to Minkowski space-time. These results suggest potential implications for the spectrum of scalar density fluctuations as well as non-gaussianities.

Particle decay in inflationary cosmology

TL;DR

This work develops a dynamical renormalization group (DRG) framework to define and compute particle decay during inflation in de Sitter space, where energy is not globally conserved. By analyzing a simple trilinear interaction between a massive decaying field and massless conformally coupled products, the authors derive DRG-improved relaxation laws for superhorizon and subhorizon modes, linking the decay rate to de Sitter features and showing enhancement relative to Minkowski space. The results reveal a decay exponent with for superhorizon modes, a Hawking-temperature interpretation, and a horizon-crossing scenario where long-wavelength power is suppressed. The findings suggest potentially measurable imprints on the primordial power spectrum and non-Gaussianities, motivating further gauge-invariant analyses of interacting perturbations during inflation.

Abstract

We investigate the relaxation and decay of a particle during inflation by implementing the dynamical renormalization group. This investigation allows us to give a meaningful definition for the decay rate in an expanding universe. As a prelude to a more general scenario, the method is applied here to study the decay of a particle in de Sitter inflation via a trilinear coupling to massless conformally coupled particles, both for wavelengths much larger and much smaller than the Hubble radius. For superhorizon modes we find that the decay is of the form eta^{Gamma1} with eta being conformal time and we give an explicit expression for Gamma1 to leading order in the coupling which has a noteworthy interpretation in terms of the Hawking temperature of de Sitter space-time. We show that if the mass M of the decaying field is << H then the decay rate during inflation is enhanced over the Minkowski spacetime result by a factor 2H/[pi M]. For wavelengths much smaller than the Hubble radius we find that the decay law is e^{-alpha/[k H C(eta)} with C(eta) the scale factor and alpha determined by the strength of the trilinear coupling. This result suggests a suppression of power for long wavelength modes upon horizon crossing. In all cases we find a substantial enhancement in the decay law as compared to Minkowski space-time. These results suggest potential implications for the spectrum of scalar density fluctuations as well as non-gaussianities.

Paper Structure

This paper contains 13 sections, 113 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The model
  3. Non-equilibrium Green's and correlation functions
  4. Equations of motion and the dynamical renormalization group
  5. Dynamical renormalization group (DRG)
  6. Specific cases
  7. Wavelengths larger than the Hubble radius: $k=0$
  8. Decay rate and mass renormalization:
  9. Minkowski space-time limit.
  10. Modes that cross the horizon during inflation $\vec{k} \neq 0~~,~~ \eta \rightarrow 0^-$
  11. Wavelengths much smaller than the Hubble radius: $|k\eta| \gg 1$:
  12. Conclusions and discussion
  13. Decay rate in Minkowski space-time:

Figures (1)

  • Figure 1: Self energy loop of conformally coupled massless particles (dashed lines).