Linearized Weyl-Weyl correlator in a de Sitter breaking gauge

Abstract

We use a de Sitter breaking graviton propagator [1,2] 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 [3], 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.

The Weyl tensor correlator in cosmological spacetimes

“…It is seen that the IR divergences, which appear for the graviton and scalar two-point functions, do not contribute to the Weyl tensor correlator, confirming thus the conjectured resolution of the IR problem in this case. The de Sitter limit of the result is taken and shown to coincide with the previous results [14][15][16][17][18]. Lastly, in section 6 we show how to recover more familiar observables such as the power spectrum from the Weyl tensor correlator, and clarify how a nearly scale-invariant spectrum arises, even if the Weyl tensor is IR-safe.…”

Graviton loop corrections to vacuum polarization in de Sitter in a general covariant gauge

“…Recall that an overlined tensor indicates the suppression of its temporal components, δ (94) can all be represented using the standard basis described in section 2.2 [95,98],…”

Excitation of photons by inflationary gravitons

“…• A computation of the linearized Weyl-Weyl correlator in both the noncovariant [81] and covariant gauges [82].…”