One-loop graviton corrections to conformal scalars on a de Sitter background

We exploit a recent computation of one graviton loop corrections to the self-mass [D. Glavan et al., Single graviton loop contribution to the self-mass of a massless, conformally coupled scalar on a de Sitter background, Phys. Rev. D 101, 106016 (2020).] to quantum correct the field equation for a massless, conformally coupled scalar on a de Sitter background. With the obvious choice for the finite part of the R2 ϕ2 counterterm, we find that neither plane wave mode functions nor the response to a point source acquires large infrared logarithms. However, we do find a decaying logarithmic correction to the mode function and a short distance logarithmic running of the potential in addition to the power-law effect inherited from flat space.