  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.
