Small scale structure predictions from discrete symmetry breaking - possible early quasar formation

We discuss the local density fluctuations which arise due to the topological defects that appear after the phase transition of light pseudo-Goldstone bosons. It has been found that in a post-inflationary universe the fluctuations of these defects at large scales may have led to galaxy formation, while being consistent with the measurements of the cosmic microwave background radiation. Here we show that at the local level, the fluctuations may be sufficiently large to lead to the production of non-linear structures at early times. Using percolation theory, we calculate the distribution of the local overdensities. We find that the number density of non-linear objects with masses of order 1013 solar masses (a typical mass scale in the models we are considering), exhibits a distribution which peaks around a value z = 2 and drops rapidly for higher redshifts. Moreover, it may be possible that a limited number of such structures are produced at redshifts of order 10. This raises the possibility of early appearance of non-linear objects like quasars. Although here we chose to work in the parameter space which is optimal for the generation of large scale structure as well, these features are generic for a wide class of domain wall models.