Resumming Inflationary Logarithms: A Higher Order Test of Starobinksy's Stochastic Formalism on de Sitter Background

In addition to proposing one of the first theories of primordial inflation, Starobinsky was the first to realize that the accelerated expansion of inflation generates a spectrum of gravitational radiation. However, calculating the Graviton loop corrections is not straight forward. Understanding what happens after the breakdown of perturbation theory requires a way of resumming the series of leading logarithms. Although Starobinsky’s stochastic formalism solves the analogous problem for the large logarithms of scalar potential models, the derivative interactions of quantum gravity cause it to fail. Nonlinear sigma models have the same derivative interactions as quantum gravity but without the indices and the gauge issue. Hence, they provide a simplified venue for working out a procedure to sum the leading logarithms. These efforts have recently resulted in a synthesis involving variants of Starobinsky’s stochastic technique with the renormalization group.

The results here show the computation of the evolution of the scalar background at two loop order, which permits a nontrivial check of the stochastic prediction, and the computation of the 1-loop beta function on de Sitter background. Furthermore, we provide the numerical computation of the late time development of scalar background on arbitrary cosmological backgrounds.