Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum

Abstract

The issue of de Sitter invariance for a massless minimally coupled scalar field is revisited. Formally, it is possible to construct a de Sitter invariant state for this case provided that the zero mode of the field is quantized properly. Here we take the point of view that this state is physically acceptable, in the sense that physical observables can be computed and have a reasonable interpretation. In particular, we use this vacuum to derive a new result: that the squared difference between the field at two points along a geodesic observer's space-time path grows linearly with the observer's proper time for a quantum state that does not break de Sitter invariance. Also, we use the Hadamard formalism to compute the renormalized expectation value of the energy momentum tensor, both in the O(4) invariant states introduced by Allen and Follaci, and in the de Sitter invariant vacuum. We find that the vacuum energy density in the O(4) invariant case is larger than in the de Sitter invariant case.

arXiv commentTUTP-92-1, to appear in Phys. Rev. D

Cited by in corpus (85)

• Non-Gaussianity in multi-field inflation
• Infrared effects in inflationary correlation functions
• Gupta-Bleuler quantization for minimally coupled scalar fields in de Sitter space
• Inflation, holography, and the choice of vacuum in de Sitter space
• On the proper treatment of massless fields in Euclidean de Sitter space
• Energy-Momentum Tensor of Particles Created in an Expanding Universe
• Loops in inflationary correlation functions
• Short distance and initial state effects in inflation: stress tensor and decoherence
• One-loop gravitational wave spectrum in de Sitter spacetime
• Attractor states and infrared scaling in de Sitter space
• Nonsingular vacuum cosmologies with a variable cosmological term
• Stress tensor fluctuations in de Sitter spacetime
• Inflationary Infrared Divergences: Geometry of the Reheating Surface vs. delta N Formalism
• Hadamard states for a scalar field in anti-de Sitter spacetime with arbitrary boundary conditions
• Scalar field instability in de Sitter space-time
• Spacelike Fluctuations of the Stress Tensor for de Sitter Vacuum
• Fluctuating geometries, q-observables, and infrared growth in inflationary spacetimes
• Adiabatic regularization of the graviton stress-energy tensor in de Sitter space-time
• Distinguished quantum states in a class of cosmological spacetimes and their Hadamard property
• Multi-horizon spherically symmetric spacetimes with several scales of vacuum energy
• Group theoretical approach to quantum fields in de Sitter space II. The complementary and discrete series
• Method to compute the stress-energy tensor for the massless spin 1/2 field in a general static spherically symmetric spacetime
• Quasi-open inflation
• Aspects of Quantum Gravity in de Sitter Spaces
• Mode-sum construction of the covariant graviton two-point function in the Poincaré patch of de Sitter space
• A Naturally Renormalized Quantum Field Theory
• Unruh response functions for scalar fields in de Sitter space
• Ghosts in a Mirror
• Vacuum polarization by a cosmic string in de Sitter spacetime
• Constructing Infrared Finite Propagators in Inflating Space-time
• Quantum Correlators in Friedmann Spacetimes -The omnipresent de Sitter and the invariant vacuum noise
• de Sitter Space is Unstable in Quantum Gravity
• Infrared Behavior of Quantum Fields in Inflationary Cosmology -- Issues and Approaches: an overview
• Studies on the SJ Vacuum in de Sitter Spacetime
• Fermionic vacuum densities in higher-dimensional de Sitter spacetime
• Eternity and the cosmological constant
• Massless Scalar Field Vacuum in de Sitter Spacetime
• QFT in the flat chart of de Sitter space
• Massless scalar fields and infrared divergences in the inflationary brane world
• Covariant and infrared-free graviton two-point function in de Sitter spacetime
• Zero mode suppression of superluminal signals in light-matter interactions
• Quantization of massive scalar fields over static black string backgrounds
• Strong restriction on inflationary vacua from the local gauge invariance III: Infrared regularity of graviton loops
• Entropy of Quantum Fields in de Sitter Space-time
• Degravitation, Inflation and the Cosmological Constant as an Afterglow
• Analytical approximation of the stress-energy tensor of a quantized scalar field in static spherically symmetric spacetimes
• Vacuum states for gravitons field in de Sitter space
• Vacuum polarization of massive spinor fields in static black-string backgrounds
• Stress energy correlator in de Sitter space-time : its conformal masking or growth in connected Friedmann universes
• Graviton physics: Quantum field theory of gravitons, graviton noise and gravitational decoherence -- a concise tutorial
• Quantum particle production near the big rip revisited
• Scale-Invariant Curvature Fluctuations from an Extended Semiclassical Gravity
• Unruh deWitt probe of late time revival of quantum correlations in Friedmann spacetimes
• Krein Spaces in de Sitter Quantum Theories
• Removing the Faddeev-Popov zero modes from Yang-Mills theory in spacetimes with compact spatial sections
• Correlation Functions of Massless Interacting Scalar Fields in de Sitter Space
• Unitary evolution of free massless fields in de Sitter space-time
• Detecting the massive bosonic zero-mode in expanding cosmological spacetimes
• Automorphic scalar fields in two-dimensional de Sitter space
• Analytical approximation for $<{\varphi }^2>$ of a quantized scalar field in ultrastatic asymptotically flat spacetimes
• Renormalized stress tensor in one-bubble spacetimes
• A discrete nonetheless remarkable brick in de Sitter: the "massless minimally coupled field"
• Quantum fluctuations in the DGP model and the size of the cross-over scale
• Non-local scalar field on deSitter and its infrared behaviour
• A relationship between scalar Green functions on hyperbolic and Euclidean Rindler spaces
• Vacuum polarization by a scalar field in de Sitter spacetime in the presence of global monopole
• Remark About dS/CFT Correspondence
• Functional formulation of quantum theory of a scalar field in a metric with Lorentzian and Euclidean signatures
• Tracking Pre-inflation Era from density perturbation spectra
• Rest frame vacua of massive Klein-Gordon fields on spatially flat FLRW spacetimes
• Scalar field in ${\mathrm{AdS}}_2$ and representations of $\widetilde{\mathrm{SL}}(2,\mathbb{R})$
• Vacua in locally de Sitter cosmologies, and how to distinguish them
• Unequal time Commutators in Friedmann universes: Deterministic evolution of massless fields
• Infrared problem in the Faddeev-Popov-ghost propagator in perturbative quantum gravity in de Sitter spacetime
• The Sine-Gordon QFT in de Sitter spacetime
• Vacuum effects induced by a plate in de Sitter spacetime in the presence of a cosmic string
• Wightman functions in de Sitter and anti-de Sitter spacetimes in the presence of cosmic string
• Vacuum fluctuation of conformally coupled scalar field in FLRW space-times
• Where do all the supercurvature modes go?
• Aspects of Quantum Fields on Causal Sets
• Infrared Divergences in dS/CFT
• Fermionic Casimir effect in de Sitter spacetime
• Local operators in the Sine-Gordon model: ${\partial }_{\mu }\varphi {\partial }_{\nu }\varphi$ and the stress tensor
• Discrete symmetries determining scalar quantum modes on the de Sitter spacetime
• Towards obtaining Green functions for a Casimir cavity in de Sitter spacetime