Gauge dependence cancels in the one-loop effective scalar equation in de Sitter when all diagram contributions including external mode corrections are collected.
Graviton Corrections to Vacuum Polarization during Inflation
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abstract
We use dimensional regularization to compute the one loop quantum gravitational contribution to the vacuum polarization on de Sitter background. Adding the appropriate BPHZ counterterms gives a fully renormalized result which can be used to quantum correct Maxwell's equations. We use the Hartree approximation to argue that the electric field strengths of photons experience a secular suppression during inflation.
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Cancellation of one-parameter graviton gauge dependence in the effective scalar field equation in de Sitter
Gauge dependence cancels in the one-loop effective scalar equation in de Sitter when all diagram contributions including external mode corrections are collected.