Phase-space distribution of volatile dark matter

We discuss the phase-space distribution of mu neutrinos if tau neutrinos are unstable and decay into nu(mu) + scalar. If this scalar is a familon or a Majoron, in the generic case the nu(mu), background is NOT the straightforward overlap of neutrinos of thermal and decay origins. A delay in nu(tau) decay, due to the Pauli exclusion principle, can modify it in a significant way. We provide the equations to calculate the to or nu(mu) distribution and show that, in some cases, there exists a good approximate solution to them. However, even when such solution is not admitted, the equations can be numerically solved following a precise pattern. We give such a solution for a number of typical cases. If nu(mu) has a mass similar to 2 eV and the see-saw argument holds, nu(tau) must be unstable and the decay into nu(mu) + scalar is a reasonable possibility. The picture leads to a delayed equivalence redshift, which could allow to reconcile COBE data with a bias parameter b greater than or equal to 1.