  We develop a covariant method for studying the effects of a reheating phase
on the primordial adiabatic and isocurvature perturbations in two-field models
of inflation. To model the decay of the scalar fields into radiation at the end
of inflation, we introduce a prescription in which radiation is treated as an
additional effective scalar field, requiring us to extend the two-field setup
into a three-field system. In this prescription, the coupling between radiation
and the scalars can be interpreted covariantly in terms geometrical quantities
that parametrize the evolution of a background trajectory in a three-field
space. In order to obtain concrete results, we consider two scenarios
characterized for having unsuppressed isocurvature fluctuations at the end of
inflation: (1) canonical two-field inflation with the product exponential
potential, which sources a large negative amount of non-gaussianity and, (2)
two-field inflation with an ultra-light field, a model in which the
isocurvature mode becomes approximately massless, and its interaction with the
curvature perturbation persists during the entire period of inflation. In both
cases we discuss how their predictions are modified by the coupling of the
scalar fields to the radiation fluid.
