Cosmological Structure Formation With and Without Hot Dark Matter
  Cold + Hot Dark Matter (CHDM) is perhaps the best theory of cosmic structure formation {\it if} the cosmological matter density is near critical (i.e., $\Omega_0 \approx 1$) and {\it if} the expansion rate is not too large (i.e. $h \equiv H_0/(100 \kmsMpc) \lsim 0.6$). I discuss CHDM together with its chief competitor among CDM variants, low-$\Omega_0$ CDM with a cosmological constant (\lcdm). \lcdm\ with $\Omega_0 \sim 0.3$ has the possible virtue of allowing a higher expansion rate $H_0$ for a given cosmic age $t_0$, but the defect of predicting too much fluctuation power on small scales. Also, except for the $H_0-t_0$ problem, there is not a shred of evidence in favor of a nonzero cosmological constant, only increasingly stringent observational upper bounds on it. CHDM has less power on small scales, in good agreement with data, although it remains to be seen whether it predicts early enough galaxy formation to be compatible with the latest high-redshift data. CHDM has the advantage among $\Omega=1$ CDM-type models of requiring little or no tilt, which appears to be an advantage in fitting recent small-angle cosmic microwave background anisotropy data. The presence of a hot component that clusters less than cold dark matter lowers the effective $\Omega_0$ that would be measured on small scales, which appears to be in accord with observations, and it may also avoid the discrepancy between the high central density of dark matter halos from CDM simulations compared to evidence from rotation curves of dwarf spiral galaxies. 
Joel Primack (University of California Santa Cruz)