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On the Decoherence of Primordial Fluctuations During Inflation

C. P. Burgess, R. Holman, D. Hoover

TL;DR

This work develops a master-equation approach to quantify how quantum inflationary perturbations become classical via environment-induced decoherence. By modeling the observable sector with the Mukhanov variable and treating sub-Hubble short-wavelength modes as the environment, the authors derive conditions under which decoherence occurs, showing that the late-time density matrix becomes diagonal in the field basis and that decoherence can arise even for gravitational-strength couplings. They find decoherence is robust to the specifics of the A–B coupling and that post-inflationary (reheating-era) thermal environments provide a particularly plausible route to decoherence before horizon re-entry, with potential observational implications if Planck-suppressed interactions are involved. The work clarifies the regimes where the master-equation is valid and argues that inflation-era decoherence is unlikely under standard BD vacua, guiding future efforts to identify the dominant decoherence sources in the early universe.

Abstract

We study the process whereby quantum cosmological perturbations become classical within inflationary cosmology. By setting up a master-equation formulation we show how quantum coherence for super-Hubble modes can be destroyed by their coupling to the environment provided by sub-Hubble modes. We identify what features the sub-Hubble environment must have in order to decohere the longer wavelengths, and identify how the onset of decoherence (and how long it takes) depends on the properties of the sub-Hubble physics which forms the environment. Our results show that the decoherence process is largely insensitive to the details of the coupling between the sub- and super-Hubble scales. They also show how locality implies, quite generally, that the decohered density matrix at late times is diagonal in the field representation (as is implicitly assumed by extant calculations of inflationary density perturbations). Our calculations also imply that decoherence can arise even for couplings which are as weak as gravitational in strength.

On the Decoherence of Primordial Fluctuations During Inflation

TL;DR

This work develops a master-equation approach to quantify how quantum inflationary perturbations become classical via environment-induced decoherence. By modeling the observable sector with the Mukhanov variable and treating sub-Hubble short-wavelength modes as the environment, the authors derive conditions under which decoherence occurs, showing that the late-time density matrix becomes diagonal in the field basis and that decoherence can arise even for gravitational-strength couplings. They find decoherence is robust to the specifics of the A–B coupling and that post-inflationary (reheating-era) thermal environments provide a particularly plausible route to decoherence before horizon re-entry, with potential observational implications if Planck-suppressed interactions are involved. The work clarifies the regimes where the master-equation is valid and argues that inflation-era decoherence is unlikely under standard BD vacua, guiding future efforts to identify the dominant decoherence sources in the early universe.

Abstract

We study the process whereby quantum cosmological perturbations become classical within inflationary cosmology. By setting up a master-equation formulation we show how quantum coherence for super-Hubble modes can be destroyed by their coupling to the environment provided by sub-Hubble modes. We identify what features the sub-Hubble environment must have in order to decohere the longer wavelengths, and identify how the onset of decoherence (and how long it takes) depends on the properties of the sub-Hubble physics which forms the environment. Our results show that the decoherence process is largely insensitive to the details of the coupling between the sub- and super-Hubble scales. They also show how locality implies, quite generally, that the decohered density matrix at late times is diagonal in the field representation (as is implicitly assumed by extant calculations of inflationary density perturbations). Our calculations also imply that decoherence can arise even for couplings which are as weak as gravitational in strength.

Paper Structure

This paper contains 21 sections, 77 equations, 1 figure.

Table of Contents

  1. Introduction and Summary
  2. Decoherence and Environments
  3. The Master Equation
  4. Solutions
  5. Decoherence in Cosmology
  6. Generalization to FRW Geometries
  7. Short-Wavelength Modes as Environment
  8. Decoherence After Reheating
  9. Decoherence During Inflation?
  10. Obstructions to Calculation
  11. Why Decoherence During Inflation is Unlikely
  12. Discussion
  13. Interactions With a Fluctuating Environment
  14. General Formulation of the Problem
  15. Microscopic Fluctuations
  16. ...and 6 more sections

Figures (1)

  • Figure 1: A cartoon of the evolution of the wavelength of a perturbation and the Hubble length vs time during inflation and afterwards. The vertical lines indicate the end of inflation, and the beginning of the subsequent reheating epoch.