  In inflationary cosmology, cosmic reheating after inflation sets the initial
conditions for the hot big bang. We investigate how CMB data can be used to
study the effective potential and couplings of the inflaton during reheating
and constrain the underlying microphysics. If there is a phase of preheating
that is driven by a parametric resonance or other instability, then the thermal
history and expansion history during the reheating era depend on a large number
of microphysical parameters in a complicated way. In this case the connection
between CMB observables and microphysical parameters can only established with
intense numerical studies. Such studies can help to improve CMB constraints on
the effective inflaton potential in specific models, but parameter degeneracies
usually make it impossible to extract meaningful best-fit values for individual
microphysical parameters. If, on the other hand, reheating is driven by
perturbative processes, then it can be possible to constrain the inflaton
couplings and the reheating temperature from CMB data. This provides an
indirect probe of fundamental microphysical parameters that most likely can
never be measured directly in the laboratory, but have an immense impact on the
evolution of the cosmos by setting the stage for the hot big bang.
