We study perturbative cosmological correlators in wavefunctionals which solve the Wheeler-DeWitt equation in asymptotically de Sitter spacetimesand were constructed in arxiv:2303.16315. Even in the G_N \rightarrow 0 limit, it is necessary to impose the gravitational Gauss law, which forces states to be de Sitter invariant. We set up Feynman rules for computing cosmological correlators in such states. We enumerate some necessary (but not sufficient) conditions that must be imposed on states and observables to avoid group-volume divergences. We provide sample computations to show that such cosmological correlators can be nontrivial even when the Hartle-Hawking wavefunction is Gaussian. We show that, in the presence of a heavy background state, it is possible to construct a class of state-dependent relational observables that approximate correlators in the Hartle-Hawking state.
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