The Weyl tensor correlator in cosmological spacetimes

Abstract

We give a general expression for the Weyl tensor two-point function in a general Friedmann-Lemaître-Robertson-Walker spacetime. We work in reduced phase space for the perturbations, i.e., quantize only the dynamical degrees of freedom without adding any gauge-fixing term. The general formula is illustrated by a calculation in slow-roll single-field inflation to first order in the slow-roll parameters $\epsilon$ and $\delta$, and the result is shown to have the correct de Sitter limit as $\epsilon ,\delta \to 0$. Furthermore, it is seen that the Weyl tensor correlation function does not suffer from infrared divergences, unlike the two-point functions of the metric and scalar field perturbations. Lastly, we show how to recover the usual tensor power spectrum from the Weyl tensor correlation function.

arXiv comment26 pages, 0 figures, matches published version

References in corpus (41)

• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• Planck 2013 results. XV. CMB power spectra and likelihood
• Planck 2013 Results. XXIV. Constraints on primordial non-Gaussianity
• The Quantum Gravitational Back-Reaction On Inflation
• Quantum Gravity Slows Inflation
• Super-Hubble de Sitter Fluctuations and the Dynamical RG
• Infrared effects in inflationary correlation functions
• Semiclassical relations and IR effects in de Sitter and slow-roll space-times
• Symmetries and Loops in Inflation
• Cosmological observables, IR growth of fluctuations, and scale-dependent anisotropies
• On Resumming Inflationary Perturbations beyond One-loop
• On Loops in Inflation III: Time Independence of zeta in Single Clock Inflation
• The covariant graviton propagator in de Sitter spacetime
• The constancy of ζin single-clock Inflation at all loops
• Infrared Propagator Corrections for Constant Deceleration
• Loops in inflationary correlation functions
• IR divergence does not affect the gauge-invariant curvature perturbation
• Can infrared gravitons screen $\Lambda$?
• One-loop gravitational wave spectrum in de Sitter spacetime
• The Zeta-Zeta Correlator Is Time Dependent
• Inflationary Correlation Functions without Infrared Divergences
• Gravitational Waves in Open de Sitter Space
• de Sitter invariance of the dS graviton vacuum
• Riemann correlator in de Sitter including loop corrections from conformal fields
• The physical graviton two-point function in de Sitter spacetime with S^3 spatial sections
• The Graviton Propagator in de Donder Gauge on de Sitter Background
• Self Regulation of Infrared Correlations for Massless Scalar Fields during Inflation
• The Perils of Analytic Continuation
• Nonperturbative semiclassical stability of de Sitter spacetime for small metric deviations
• Graviton Propagator in a General Invariant Gauge on de Sitter
• The Weyl tensor two-point function in de Sitter spacetime
• Generation of gravitational waves by generic sources in de Sitter space-time
• Weyl-Weyl Correlator in de Donder Gauge on de Sitter
• Linearized Weyl-Weyl Correlator in a de Sitter Breaking Gauge
• Constructing Infrared Finite Propagators in Inflating Space-time
• IR Divergences in Inflation and Entropy Perturbations
• A graviton propagator for inflation
• Infrared-finite graviton two-point function in static de Sitter space
• On cosmic hair and "de Sitter breaking" in linearized quantum gravity
• Strong restriction on inflationary vacua from the local gauge invariance III: Infrared regularity of graviton loops
• Equivalence between the Weyl-tensor and gauge-invariant graviton two-point functions in Minkowski and de Sitter spaces

Cited by in corpus (18)

• Mode-sum construction of the covariant graviton two-point function in the Poincaré patch of de Sitter space
• Summing Inflationary Logarithms in Nonlinear Sigma Models
• Large Logarithms from Quantum Gravitational Corrections to a Massless, Minimally Coupled Scalar on de Sitter
• Propagators for gauge-invariant observables in cosmology
• Fractal Spacetimes in Stochastic Gravity? -- Views from Anomalous Diffusion and the Correlation Hierarchy
• Quantum gravity corrections to the conformally coupled scalar self-mass-squared on de Sitter II: kinetic-conformal cross terms
• Cosmological Perturbations and Invariant Observables in Geodesic Lightcone Coordinates
• Compactly supported linearised observables in single-field inflation
• Single Graviton Loop Contribution to the Self-Mass of a Massless, Conformally Coupled Scalar on de Sitter Background
• Quantum gravitational corrections for spinning particles
• Infrared divergences for free quantum fields in cosmological spacetimes
• Removing the Faddeev-Popov zero modes from Yang-Mills theory in spacetimes with compact spatial sections
• Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime
• `Hidden' symmetry of linearized gravity in de Sitter space
• Scale and Conformal Invariance on (A)dS
• Causality Implies Inflationary Back-Reaction
• Conformally-related Einstein-Langevin equations for metric fluctuations in stochastic gravity
• Some Inconvenient Truths