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

Abstract

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 counterterms, 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.

One loop corrected conformally coupled scalar mode equations during inflation

“…• For quantum gravity plus electrodynamics, inflationary gravitons induce secular effects on the dynamical photons and alter the electric field of a point charge and the magnetic field of a point magnetic dipole [24][25][26][27][28][29][30].…”

Breaking of scaling symmetry by massless scalar on de Sitter

“…The first line in this expansion comes from the first line of the full solution (10), and reproduces the massless solution (5) up to a constant. The second line above comes from the small mass expansion of the second line in (10). It is clear there is no singularity at the horizon even in this limit.…”

de Sitter space is unstable in quantum gravity

“…Since the de Sitter invariant propagator has the issues described above, they use a non invariant propagator (which satisfies the same differential equation as the de Sitter propagator, but does not have the full de Sitter invariance). The analysis [41] however shows that an explicit non-invariant counterterm is required to cancel a loop divergence. Whether such a term is allowed in a consistent theory is unclear-explicit symmetry breaking in a gauge theory typically leads to violations of renormalizability and unitarity.…”

“…(3) Woodard and collaborators have suggested that the correct approach is to modify the graviton propagator ab initio (a few of these papers are [39][40][41]). Since the de Sitter invariant propagator has the issues described above, they use a non invariant propagator (which satisfies the same differential equation as the de Sitter propagator, but does not have the full de Sitter invariance).…”