On the one-loop corrections to gravitons in de Sitter space induced by massive non-minimally coupled scalars

Abstract

The graviton self-energy captures how quantum effects modify the dynamics of gravity itself. These corrections, induced by quantum matter fields, are expected to influence the evolution of gravitational perturbations during cosmic inflation to form the large-scale structure of the Universe we observe today. Previous studies have focused on one-loop corrections from scalar fields have been studied, which was extended in the master thesis by Riley Kavanagh to massive, non-minimally coupled scalars in a de Sitter spacetime, an idealized model for inflation. We will further investigate this calculation, which involves renormalization to one loop order of the graviton self-energy using the method of minimal derivative extraction. In flat spacetime, we verify that this method agrees with momentum space calculations. In de Sitter space, we point out that the use of a bilocal metric in derivation of the counterterms is unnecessary, but we have not succeeded in completing renormalization without it. Finally, we study the important property of transversality that the self-energy should satisfy but which is not manifest in de Sitter space. However, our results are not transverse, which motives further research on both transversality and renormalization.