Quantum Correlators in Friedmann Spacetimes -The omnipresent de Sitter and the invariant vacuum noise

Abstract

We discuss several aspects of quantum field theory of a scalar field in a Friedmann universe, clarifying and highlighting several conceptual and technical issues. (A) We show that one can map the dynamics of (1) a massless scalar field in a universe with power law expansion to (2) a massive scalar field in the de Sitter spacetime, which allows us to understand several features of either system and clarifies several issues related to the massless limit. (B) We obtain a useful integral representation for the Euclidean Green's function for the de Sitter spacetime, by relating it to the solution of a hypothetical electrostatic problem in five dimensions. This is helpful in the study of several relevant limits. (C) We recover that in any Friedmann universe, sourced by a negative pressure fluid, the Wightman function for a massless scalar field is divergent. This shows that the divergence of Wightman function for the massless field in the de Sitter spacetime is just a special, limiting, case of this general phenomenon. (D) We provide a generally covariant procedure for defining the power spectrum of vacuum fluctuations in terms of the different Killing vectors present in the spacetime. This allows one to study the interplay of the choice of vacuum state and the nature of the power spectrum in different coordinate systems, in the de Sitter universe, in a unified manner. (Truncated Abstract; see the paper for full Abstract.)

arXiv commentPublished version

References in corpus (42)

• Quantum effects can render w<-1 on cosmological scales
• Two-point Functions and Quantum Fields in de Sitter Universe
• Quantum fields in curved spacetime
• The IR stability of de Sitter: Loop corrections to scalar propagators
• Non-perturbative effects of vacuum energy on the recent expansion of the universe
• Infrared Sensitivity of Unstable Vacua
• Lecture notes on interacting quantum fields in de Sitter space
• Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum
• On the Instability of Global de Sitter Space to Particle Creation
• Infrared Propagator Corrections for Constant Deceleration
• Loops in inflationary correlation functions
• De Sitter Breaking through Infrared Divergences
• Infrared instability of the de Sitter space
• Stress tensor fluctuations in de Sitter spacetime
• On Infrared Effects in de~Sitter Background
• Graviton Propagator in a General Invariant Gauge on de Sitter
• Quantum Field Theory in Curved Spacetime
• Weyl-Weyl Correlator in de Donder Gauge on de Sitter
• The Power Spectrum in de Sitter Inflation, Revisited
• Linearized Weyl-Weyl Correlator in a de Sitter Breaking Gauge
• Quantization of the massless minimally coupled scalar field and the dS/CFT correspondence
• Physical meaning and consequences of the loop IR divergences in global dS
• Unruh response functions for scalar fields in de Sitter space
• Quantum Scalar Corrections to the Gravitational Potentials on de Sitter Background
• Quantum field theory in de Sitter and quasi-de Sitter spacetimes: Revisited
• The Coincidence Limit of the Graviton Propagator in de Donder Gauge on de Sitter Background
• Do We Really Understand the Cosmos?
• Propagators in de Sitter space
• One-loop quantum electrodynamic correction to the gravitational potentials on de Sitter spacetime
• Propagators for gauge-invariant observables in cosmology
• Cosmic fluctuations from quantum effective action
• Ultraviolet Regularisation in de Sitter Space
• Massless Scalar Field Vacuum in de Sitter Spacetime
• Computing the Primordial Power Spectra Directly
• Massless scalar fields and infrared divergences in the inflationary brane world
• The graviton one-loop effective action in cosmological space-times with constant deceleration
• Light scalars on cosmological backgrounds
• Infrared divergences for free quantum fields in cosmological spacetimes
• Graviton one-loop effective action and inflationary dynamics
• Two-point Correlation Functions in Inhomogeneous and Anisotropic Cosmologies
• Can observations look back to the beginning of inflation?
• From Non-trivial Geometries to Power Spectra and Vice Versa

Cited by in corpus (16)

• Cosmological and black hole islands in multi-event horizon spacetimes
• Gravity and Quantum Theory: Domains of Conflict and Contact
• Particle creation by de Sitter black holes revisited
• Finding origins of CMB anomalies in the inflationary quantum fluctuations
• Generalized Schwinger effect and particle production in an expanding universe
• Stress energy correlator in de Sitter space-time : its conformal masking or growth in connected Friedmann universes
• Thermality of the Rindler horizon: A simple derivation from the structure of the inertial propagator
• Unruh deWitt probe of late time revival of quantum correlations in Friedmann spacetimes
• Emergent $\alpha$-like fermionic vacuum structure and entanglement in the hyperbolic de Sitter spacetime
• Unequal time Commutators in Friedmann universes: Deterministic evolution of massless fields
• Bouncing and collapsing universes dual to late-time cosmological models
• A Measure for Quantum Paths, Gravity and Spacetime Microstructure
• Quadratic gravity potentials in de Sitter spacetime from Feynman diagrams
• Massless Fermions in planar Bianchi type I universes: Exact and approximate solutions
• Fluctuations in the stress energy tensor of spinor fields evolving in general FRW spacetimes
• De Sitter scattering amplitudes in the Born approximation