  The sensitivity of inflationary spectra to initial conditions is addressed in
the context of a phenomenological model that breaks Lorentz invariance by
dissipative effects above some threshold energy $\Lambda$. These effects are
obtained dynamically by coupling the fluctuation modes to extra degrees of
freedom which are unobservable below $\Lambda$. Because of the strong
dissipative effects in the early propagation, only the state of the extra
degrees of freedom is relevant for the power spectrum. If this state is the
ground state, and if $\Lambda$ is much larger than the Hubble scale $H$, the
standard spectrum is recovered. Using analytical and numerical methods, we
calculate the modifications for a large class of dissipative models. For all of
these, we show that the leading modification (in an expansion in $H/\Lambda$)
is linear in the decay rate evaluated at horizon exit, and that high frequency
superimposed oscillations are not generated. The modification is negative when
the decay rate decreases slower than the cube of $H$, which means that there is
a loss of power on the largest scales.
