Summing Large Logarithms from Loops of Inflationary Gravitons

Quantum gravitational corrections on flat space background do not affect particle kinematics at all, and only make fractional changes of order $G/r^2$ to long range forces. The situation during inflation is very different because (1) the Hubble parameter H allows fractional corrections of the form $G H^2$ and (2) the continuous production of inflationary gravitons introduces a secular element. As a result, corrections to both particle kinematics and long range forces typically grow like logarithms of the scale factor and/or the spatial separation. If inflation persists long enough, this growth must eventually cause perturbation theory to break down, begging the question of what happens next. I report on recent progress in summing the very similar large logarithms which occur in nonlinear sigma models by combining a variant of Starobinsky's stochastic formalism with a variant of the renormalization group. I discuss how this technique can be generalized to quantum gravity.
This talk is based on arXiv:2110.08715