Linearized Weyl-Weyl Correlator in a de Sitter Breaking Gauge

We use a de Sitter breaking graviton propagator to compute the tree order correlator between noncoincident Weyl tensors on a locally de Sitter background. An explicit, and very simple result is obtained, for any spacetime dimension D, in terms of a de Sitter invariant length function and the tensor basis constructed from the metric and derivatives of this length function. Our answer does not agree with the one derived previously by Kouris, but that result must be incorrect because it not transverse and lacks some of the algebraic symmetries of the Weyl tensor. Taking the coincidence limit of our result (with dimensional regularization) and contracting the indices gives the expectation value of the square of the Weyl tensor at lowest order. We propose the next order computation of this as a true test of de Sitter invariance in quantum gravity.