One-loop gravitational wave spectrum in de Sitter spacetime

Abstract

The two-point function for tensor metric perturbations around de Sitter spacetime including one-loop corrections from massless conformally coupled scalar fields is calculated exactly. We work in the Poincaré patch (with spatially flat sections) and employ dimensional regularization for the renormalization process. Unlike previous studies we obtain the result for arbitrary time separations rather than just equal times. Moreover, in contrast to existing results for tensor perturbations, ours is manifestly invariant with respect to the subgroup of de Sitter isometries corresponding to a simultaneous time translation and rescaling of the spatial coordinates. Having selected the right initial state for the interacting theory via an appropriate iεprescription is crucial for that. Finally, we show that although the two-point function is a well-defined spacetime distribution, the equal-time limit of its spatial Fourier transform is divergent. Therefore, contrary to the well-defined distribution for arbitrary time separations, the power spectrum is strictly speaking ill-defined when loop corrections are included.

42 pages, 2 figures, includes three new paragraphs in response to referee's comments

References in corpus (47)

• An Alternative to Compactification
• Quantum Contributions to Cosmological Correlations
• Quantum Gravity in Everyday Life: General Relativity as an Effective Field Theory
• Generalized metric formulation of double field theory
• AdS/CFT and gravity
• Does backreaction enforce the averaged null energy condition in semiclassical gravity?
• The Quantum Gravitational Back-Reaction On Inflation
• G-Bounce
• Observables in effective gravity
• Non-Equilibrium Quantum Fields in the Large N Expansion
• Einstein Equation with Quantum Corrections Reduced to Second Order
• Decay of Vacuum Energy
• The IR stability of de Sitter: Loop corrections to scalar propagators
• Stochastic Gravity: Theory and Applications
• Infrared Sensitivity of Unstable Vacua
• Stochastic Gravity: Theory and Applications
• Massless Minimally Coupled Fields in De Sitter Space: O(4)-Symmetric States Versus De Sitter Invariant Vacuum
• Semiclassical Equations for Weakly Inhomogeneous Cosmologies
• The "in-in" Formalism and Cosmological Perturbations
• On the proper treatment of massless fields in Euclidean de Sitter space
• Stochastic semiclassical equations for weakly inhomogeneous cosmologies
• On the Equivalence between Euclidean and In-In Formalisms in de Sitter QFT
• Stochastic semiclassical gravity
• Stochastic description for open quantum systems
• On Loops in Inflation II: IR Effects in Single Clock Inflation
• Stochastic semiclassical fluctuations in Minkowski spacetime
• Massless interacting quantum fields in deSitter spacetime
• Stochastic Gravity
• Stochastic Gravity: A Primer with Applications
• IR divergence does not affect the gauge-invariant curvature perturbation
• Induced quantum metric fluctuations and the validity of semiclassical gravity
• Lifetime of a massive particle in a de Sitter universe
• Interacting Field Theories in de Sitter Space are Non-Unitary
• A Note on Hartle-Hawking Vacua
• Metric fluctuations of an evaporating black hole from back reaction of stress tensor fluctuations
• Quantum Cosmological Correlations in an Inflating Universe: Can fermion and gauge fields loops give a scale free spectrum?
• Nonperturbative semiclassical stability of de Sitter spacetime for small metric deviations
• On the Decay of Massive Fields in de Sitter
• Scalar Contribution to the Graviton Self-Energy during Inflation
• Classical radiation by free-falling charges in de Sitter spacetime
• Backreaction from non-conformal quantum fields in de Sitter spacetime
• Noise kernel for a quantum field in Schwarzschild spacetime under the Gaussian approximation
• Inflationary Scalars Don't Affect Gravitons at One Loop
• A conformally coupled massive scalar field in the de Sitter expanding universe with the mass term treated as a perturbation
• Gravity Waves from Quantum Stress Tensor Fluctuations in Inflation
• Comments on the vacuum energy decay
• Graviton production in non-inflationary cosmology

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• The Redshift-Space Momentum Power Spectrum I: Optimal Estimation From Peculiar Velocity Surveys
• Quantum Scalar Corrections to the Gravitational Potentials on de Sitter Background
• Universal signature of quantum entanglement across cosmological distances
• Mode-sum construction of the two-point functions for the Stueckelberg vector fields in the Poincaré patch of de Sitter space
• Non-commutative Geometry from Perturbative Quantum Gravity
• One-loop quantum electrodynamic correction to the gravitational potentials on de Sitter spacetime
• Wide-angle redshift-space distortions at quasi-linear scales: cross-correlation functions from Zel'dovich approximation
• Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy
• The Weyl tensor correlator in cosmological spacetimes
• CFTs Blueshift Tensor Fluctuations Universally
• Gravitational Radiation in Quantum Gravity
• Infrared Behavior of Quantum Fields in Inflationary Cosmology -- Issues and Approaches: an overview
• Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter II: kinetic-conformal cross terms
• Tensor instabilities at the end of the LCDM universe
• Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter background
• Infrared-finite graviton two-point function in static de Sitter space
• Compactly supported linearised observables in single-field inflation
• Massless Scalar Field Vacuum in de Sitter Spacetime
• Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for ${\gamma }_{\ast }$
• Quantum corrections for spinning particles in de Sitter
• On $i\epsilon$ Prescription in Cosmology
• Instability of De Sitter Spacetime induced by Quantum Conformal Anomaly
• Our Universe from the cosmological constant
• One-loop quantum gravitational backreaction on the local Hubble rate
• Alternate Definitions of Loop Corrections to the Primordial Power Spectra
• Scale-Invariant Curvature Fluctuations from an Extended Semiclassical Gravity
• Graviton backreaction on the local cosmological expansion in slow-roll inflation
• Stationary Phase Approximation and Instanton-like States for Cosmological In-In Path Integrals
• Fully renormalized stress tensor correlator in flat space
• Dynamical Response of an Unruh-DeWitt Detector in a Quantum Field over the History of the Universe
• Correspondences of matter fluctuations in semiclassical and classical gravity for cosmological spacetime-II
• Quantum Stress Tensor Fluctuations and Primordial Gravity Waves
• Covariant Predictions for Planck-Scale Features in Primordial Power Spectra
• Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity