  We present a new systematic analysis of the early radiation era solution in
an interacting dark energy model to find the adiabatic initial conditions for
the Boltzmann integration. In a model where the interaction is proportional to
the dark matter density, adiabatic initial conditions and viable cosmologies
are possible if the early-time dark energy equation of state parameter is $w_e
> -4/5$. We find that when adiabaticity between cold dark matter, baryons,
neutrinos and photons is demanded, the dark energy component satisfies
automatically the adiabaticity condition. As supernovae Ia or baryon acoustic
oscillation data require the recent-time equation of state parameter to be more
negative, we consider a time-varying equation of state in our model. In a
companion paper [arXiv:0907.4987] we apply the initial conditions derived here,
and perform a full Monte Carlo Markov Chain likelihood analysis of this model.
