On cosmic hair and "de Sitter breaking" in linearized quantum gravity

Abstract

We quantize linearized Einstein-Hilbert gravity on de Sitter backgrounds in a covariant gauge. We verify the existence of a maximally-symmetric (i.e.de Sitter-invariant) Hadamard state $\Omega$ for all globally hyperbolic de Sitter backgrounds in all spacetime dimensions $D\ge 4$ by constructing the state's 2-point function in closed form. This 2-pt function is explicitly maximally symmetric. We prove an analogue of the Reeh-Schlieder theorem for linearized gravity. Using these results we prove a cosmic no-hair theorem for linearized gravitons: for any state in the Hilbert space constructed from $\Omega$, the late-time behavior of local observable correlation functions reduces to those of $\Omega$ at an exponential rate with respect to proper time. We also provide the explicitly maximally-symmetric graviton 2-pt functions in a class of generalized de Donder gauges suitable for use in non-linear perturbation theory. Along the way we clarify a few technical aspects which led previous authors to conclude that these 2-pt functions do not exist.

40 p., 4 figures. v2: minor typos corrected, some clarifying comments added. Results unchanged

References in corpus (8)

• The IR stability of de Sitter: Loop corrections to scalar propagators
• Semiclassical relations and IR effects in de Sitter and slow-roll space-times
• IR divergence does not affect the gauge-invariant curvature perturbation
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Cited by in corpus (10)

• The Perils of Analytic Continuation
• de Sitter tachyons and related topics
• 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
• Nonperturbative infrared enhancement of nonGaussian correlators in de Sitter space
• Hartree Approximation to the One Loop Quantum Gravitational Correction to the Graviton Mode Function on de Sitter
• The Weyl tensor correlator in cosmological spacetimes
• Single Graviton Loop Contribution to the Self-Mass of a Massless, Conformally Coupled Scalar on de Sitter Background
• `Hidden' symmetry of linearized gravity in de Sitter space
• Fully renormalized stress tensor correlator in flat space