  We evaluate one loop quantum gravity corrections to the conformally coupled
(CC) scalar self-mass-squared on a locally de Sitter background. In this paper
we consider only the conformal-conformal interaction part of the
self-mass-squared. This complements the minimal-minimal part worked out in the
previous paper [E. O. Kahya and R. P. Woodard, Phys. Rev. D 76, 124005 (2007),
arXiv: 0709.0536], and we will add the minimal-conformal part in a follow-up
paper to complete the full self-mass-squared at one loop order. The computation
is performed using dimensional regularization and the results are fully
renormalized by absorbing divergences with counterterms. The finite results can
give rise to quantum corrections to the CC scalar mode functions and therefore
to their power spectra.
