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

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.