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We quantize linearized Einstein-Hilbert gravity on de Sitter backgrounds in acovariant gauge. We verify the existence of a maximally-symmetric (i.e.deSitter-invariant) Hadamard state $\Omega$ for all globally hyperbolic de Sitterbackgrounds in all spacetime dimensions $D \ge 4$ by constructing the state's2-point function in closed form. This 2-pt function is explicitly maximallysymmetric. We prove an analogue of the Reeh-Schlieder theorem for linearizedgravity. Using these results we prove a cosmic no-hair theorem for linearizedgravitons: for any state in the Hilbert space constructed from $\Omega$, thelate-time behavior of local observable correlation functions reduces to thoseof $\Omega$ at an exponential rate with respect to proper time. We also providethe explicitly maximally-symmetric graviton 2-pt functions in a class ofgeneralized de Donder gauges suitable for use in non-linear perturbationtheory. Along the way we clarify a few technical aspects which led previousauthors to conclude that these 2-pt functions do not exist.

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