Do Galactic Systems Form Too Late in Cold+Hot Dark Matter Models?
  The abundance of galactic systems at high redshifts can impose a strong constraint on the cold+hot dark matter (CDM+HDM) models. The hot component reduces the excessive small-scale power in the COBE-normalized CDM model but also delays the epoch of galaxy formation. We present results from the first numerical simulations that have enough dynamic range to address accurately the issue of high-redshift halo abundances in CDM+HDM models. Equivalent high-resolution particle-particle/particle-mesh $N$-body simulations are performed for spatially flat models with $\Omega_\nu =0.3$ and 0.2 (with $H_0=50$ km s$^{-1}$ Mpc$^{-1}$ and $\Omega_b=0.05$). We study the constraints placed on the models by the high-redshift quasar space density and by the mass fraction in neutral dense gas associated with damped Ly$\alpha$ systems. We find that even with optimistic assumptions, the much-studied $\Omega_\nu=0.3$ model does not produce enough massive halos to account for the observed abundance of quasars at $z>4$. The model passes this test if $\Omega_\nu$ is decreased to 0.2. Both models do not produce enough high column-density halos to account for the amount of gas in damped Ly$\alpha$ systems at $z\go 3$: the $\Omega_\nu=0.3$ model falls short by a factor $\sim$80; the $\Omega_\nu=0.2$ model by a factor $\sim$3. We conclude that only CDM+HDM models with $\Omega_\nu\lo 0.2$ can match observations at high redshift, implying an upper bound of 4.7 eV on the most massive light neutrino (presumably the $\tau$). 
Chung-Pei Ma and Edmund Bertschinger