We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ c
ounterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop. A number of identities are derived which should facilitate further graviton loop computations.
We calculate the one-loop corrections from inflationary gravitons to the electromagnetic fields of a point charge and a point magnetic dipole on a locally de Sitter space background. Results are obtained both for an observer at rest in co-moving coor
dinates, whose physical distance from the sources increases with the expanding universe, and for an observer at rest in static coordinates, whose physical distance from the sources is constant. The fields of both sources show the de Sitter analogs of the fractional $G/r^2$ corrections which occur in flat space, but there are also some fractional $G H^2$ corrections due to the scattering of virtual photons from the vast ensemble of infrared gravitons produced by inflation. The co-moving observer perceives the magnitude of the point charge to increase linearly with co-moving time and logarithmically with the co-moving position, however, the magnetic dipole shows only a negative logarithmic spatial variation. The static observer perceives no secular change of the point charge but he does report a secular enhancement of the magnetic dipole moment.
A nice paper by Morrison demonstrates the recent convergence of opinion that has taken place concerning the graviton propagator on de Sitter background. We here discuss the few points which remain under dispute. First, the inevitable decay of tachyon
ic scalars really does result in their 2-point functions breaking de Sitter invariance. This is obscured by analytic continuation techniques which produce formal solutions to the propagator equation that are not propagators. Second, Morrisons de Sitter invariant solution for the spin two sector of the graviton propagator involves derivatives of the scalar propagator at $M^2 = 0$, where it is not meromorphic unless de Sitter breaking is permitted. Third, de Sitter breaking does not require zero modes. Fourth, the ambiguity Morrison claims in the equation for the spin two structure function is fixed by requiring it to derive from a mode sum. Fifth, Morrisons spin two sector is not physically equivalent to ours because their coincidence limits differ. Finally, it is only the noninvariant propagator that gets the time independence and scale invariance of the tensor power spectrum correctly.
