An effective field theory during inflation: reduced density matrix and its quantum master equation

Abstract

We study the power spectrum of super-Hubble fluctuations of an inflaton-like scalar field, the "system", coupled to another scalar field, the "environment" during de Sitter inflation. We obtain the reduced density matrix for the inflaton fluctuations by integrating out the environmental degrees of freedom. These are considered to be massless and conformally coupled to gravity as a \emph{proxy} to describe degrees of freedom that remain sub-Hubble all throughout inflation. The time evolution of the density matrix is described by a quantum master equation, which describes the decay of the vacuum state, the production of particles and correlated pairs and quantum entanglement between super and sub-Hubble degrees of freedom. The quantum master equation provides a non-perturbative resummation of secular terms from self-energy (loop) corrections to the inflaton fluctuations. In the case studied here these are Sudakov-type double logarithms which result in the \emph{decay} of the power spectrum of inflaton fluctuations upon horizon crossing with a concomitant violation of scale invariance. The reduced density matrix and its quantum master equation furnish a powerful non-perturbative framework to study the effective field theory of long wavelength fluctuations by tracing short wavelength degrees of freedom.

26 pages, 3 figs, extended discussion,

References in corpus (23)

• Nonperturbative Dynamics Of Reheating After Inflation: A Review
• Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?
• Stochastic Inflationary Scalar Electrodynamics
• Semiclassical relations and IR effects in de Sitter and slow-roll space-times
• Leading Log Solution for Inflationary Yukawa
• Breakdown of Semiclassical Methods in de Sitter Space
• Heavy fields, reduced speeds of sound and decoupling during inflation
• On Resumming Inflationary Perturbations beyond One-loop
• On the proper treatment of massless fields in Euclidean de Sitter space
• On the Decoherence of Primordial Fluctuations During Inflation
• Classical approximation to quantum cosmological correlations
• Reply to `Can infrared gravitons screen $\Lambda$?'
• Infrared Propagator Corrections for Constant Deceleration
• Fermion Mass Generation in de Sitter Space
• The Zeta-Zeta Correlator Is Time Dependent
• Interacting Field Theories in de Sitter Space are Non-Unitary
• Effective Field Theory out of Equilibrium: Brownian quantum fields
• Condensates and quasiparticles in inflationary cosmology: mass generation and decay widths
• Vacuum Fluctuations of a Scalar Field during Inflation: Quantum versus Stochastic Analysis
• On the Perturbative Stability of Quantum Field Theories in de Sitter Space
• Classical radiation by free-falling charges in de Sitter spacetime
• Spontaneous symmetry breaking in inflationary cosmology: on the fate of Goldstone Bosons
• Radiative Corrections from Heavy Fast-Roll Fields during Inflation

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