  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.
