Graviton 1-loop corrections from massive non-minimally coupled scalar fields in de-Sitter background
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Quantum one-loop corrections to various propagators on a de-Sitter background have been extensively studied by Woodard, Park, Prokopec and collaborators . In the current master thesis, we investigate the one-loop corrections to the graviton propagator due to the presence of massive non-minimally coupled scalar fields. Our background geometry is the open conformal coordinate patch of de-Sitter spacetime. We define the graviton to be a small fluctuation around the de-Sitter background while the massive non-minimally coupled scalar propagator is the so-called Chernikov-Tagirov propagator. Two Feynman diagrams contribute to the self-energy of the graviton. The quartic contribution, which corresponds to local contribution, has already been renormalized by R. Koelewijn (”Gravitons on de Sitter modified by quantum fluctuations of a nonminimally coupled massive scalar. MS thesis. 2017.” ). We focus our attention to the cubic contribution (non-local) which is proportial to the TT correlator computed by R.Koelewijn. Our aim is to reorganize the expression for the TT correlator in such a way that it will allow us to renormalize it, using dimensional regularization scheme. In particular, we localize the divergences that appear onto local δ-function terms, and subtract them by using the local counterterms R2 and C2 introduced in the 80’s by G. t’Hooft and M.Veltman. Since our final goal is to quantum correct the linearized Einstein’s equations, the final form of the graviton self energy should contain only terms which are integrable in D = 4 dimensions and finite.