  In this paper, we explore a novel observational signature of gravitational
corrections during slow-roll inflation. We study the coupling of the inflaton
field to higher-curvature tensors in models with a minimal breaking of
conformal symmetry. In that case, the most general correction to the tensor
two-point function is captured by a coupling to the square of the Weyl tensor.
We show that these scenarios lead to a correction to the tilt of the tensor
power spectrum and hence a violation of the tensor consistency condition. We
arrive at the same conclusion through an analysis in conformal perturbation
theory.
