On the Expected Backreaction During Preheating

In previous work we argued that the correct procedure to predict the gravitational wave signal from preheating after inflation rests on the in-in formalism. We extend here our previous analysis to include the backreaction of the produced matter on the motion of the inflaton and the expansion of the universe, and study how the latter affect the spectrum of the resulting gravitational waves. The addition of backreaction demands the appropriate renormalization of divergent expectation values, which we regularize by preserving diffeomorphism invariance in a manner that is amenable to numerical integration. The very same calculation also allows us to determine for which strength of the inflaton to matter couplings reheating is successful. We illustrate our results with the scalar version of the Starobinsky model of inflation, and observe that it is hard to reheat the universe while keeping radiative corrections under control.