On the breakdown of the curvature perturbation ζ during reheating

Abstract: It is known that in single scalar field inflationary models the standard curvature perturbation \zeta, which is supposedly conserved at superhorizon scales, diverges during reheating at times d\Phi/dt=0, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge \phi=0, where \phi\ denotes the inflaton perturbation, breaks down when d\Phi/dt=0. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of \zeta\ is ill posed mathematically. We solve this problem in the free theory by introducing a family of smooth gauges that still eliminates the inflaton fluctuation \phi\ in the Hamiltonian formalism and gives a well behaved curvature perturbation \zeta, which is now rigorously conserved at superhorizon scales. At the linearized level, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for the inflationary predictions.