  We study the growth of density perturbations in a universe with unstable dark
matter particles. The mass (m_\nu) range 30 eV < m_\nu < 10 keV with lifetimes
($t_d$) in the range 10^7 sec < t_d < 10^16 sec are considered. We calculate
the COBE normalized matter power spectrum for these models. We find that it is
possible to construct models consistent with observations for masses $m_\nu >
50 eV by adjusting t_d so as to keep the quantity (m_\nu(keV))^2 t_d(yr)
constant at a value around 100. For m_\nu < 1 keV the power spectrum has extra
power at small scales which could result in an early epoch of galaxy formation.
We do not find any value of t_d which gives a viable model in the mass range
m_\nu < 50 eV. We also consider the implications of radiatively decaying
neutrinos---models in which a small fraction B << 1 of neutrinos decay into
photons-which could possibly ionize the intergalactic medium (IGM) at high
redshift. We show that the parameter space of decaying particles which
satisfies the IGM observations does not give viable models of structure
formation.
