  It has recently been suggested that collapse of neutron stars induced by a
phase transition to quark matter can be a considerable source of gravitational
waves with kHz frequencies. We demonstrate that if about one percent of all
neutron stars undergo this process, the resulting cosmological gravitational
wave background would reach about 10^-10 times the critical density. The
background would peak at kHz frequencies and could have an observationally
significant tail down to Hz frequencies. It would be comparable or higher than
other astrophysical backgrounds, for example, from ordinary core collapse
supernovae, from r-mode instabilities in rapidly rotating neutron stars, or
from magnetars. The scenario is consistent with cosmological backgrounds in
neutrinos and photons.
