  We study the evironment-induced decoherence of cosmological perturbations in
an inflationary background. Splitting our spectrum of perturbations into two
distinct sets characterized by their wavelengths (super and sub-Hubble), we
identify the long wavelength modes with our system and the remainder with an
environment. We examine the effects of the interactions between our system and
the environment. This interaction causes the long-wavelength modes to decohere
for realistic values of the coupling and we conclude that interactions due to
backreaction are more than sufficient to decohere the system within 60
e-foldings of inflation. This is shown explicitly by obtaining an analytic
solution to a master equation detailing the evolution of the density matrix of
the system.
