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My project computed the one loop fermion self-energy for massless Dirac +Einstein in the presence of a locally de Sitter background. I employeddimensional regularization and obtain a fully renormalized result by absorbingall divergences with Bogliubov, Parasiuk, Hepp and Zimmermann (BPHZ)counterterms. An interesting technical aspect of my computation was the needfor a noninvariant counterterm, owing to the breaking of de Sitter invarianceby our gauge condition. I also solved the effective Dirac equation for masslessfermions during inflation in the simplest gauge, including all one loopcorrections from quantum gravity. At late times the result for a spatial planewave behaves as if the classical solution were subjected to a time-dependentfield strength renormalization of Z_2(t) = 1 - 17(4 pi) *G H^2 *ln(a) + O(G^2).I showed that this also follows from making the Hartree approximation, althoughthe numerical coefficients differ.

The Quantum-Corrected Fermion Mode Function during Inflation