3.4. Problems with DM

A number of potential problems with the neutrino dominated universe had emerged by about 1983, however.

• From studies both of nonlinear clustering [48, 50] (comoving length scale 10 Mpc) and of streaming velocities [51] in the linear regime ( > 10 Mpc), it follows that supercluster collapse must have occurred recently: z_sc 0.5 is indicated and in any case z_sc < 2 [48]. However, the best limits on galaxy ages coming from globular clusters and other stellar populations indicated that galaxy formation took place before z 3. Moreover, if quasars are associated with galaxies, as is suggested by the detection of galactic luminosity around nearby quasars and the apparent association of more distant quasars with galaxy clusters, the abundance of quasars at z > 2 was also inconsistent with the ``top-down'' neutrino dominated scheme in which superclusters form first: z_sc > z_galaxies.

• Numerical simulations of the nonlinear ``pancake'' collapse taking into account dissipation of the baryonic matter showed that at least 85% of the baryons are so heated by the associated shock that they remain unable to condense, attract neutrino halos, and eventually form galaxies [5, 52]. This was a problem for the hot DM scheme for two reasons. With the primordial nucleosynthesis constraint _b 0.1, there would be difficulty having enough baryonic matter condense to form the luminosity that we actually observe. And, where are the X-rays from the shock-heated pancakes [53]?

• The neutrino picture predicts [54] that there should be a factor of ~ 5 increase in M / M_b between large galaxies (M ~ 10¹² M) and large clusters (M 10¹⁴ M), since the larger clusters, with their higher escape velocities, are able to trap a considerably larger fraction of the neutrinos. Although there is some indication that the mass-to-light ratio M/L increases with M, the ratio of total to luminous mass M / M_lum is probably a better indicator of the value of M /M_b, and it is roughly the same for galaxies with large halos and for rich clusters.

These problems, while serious, would perhaps not have been fatal for the hot DM scheme. But an even more serious problem for HDM arose from the low amplitude of the CMB fluctuations detected by the COBE satellite, (T / T)_rms = (1.1 ± 0.2) x 10^-5 smoothed on an angular scale of about 10° [55]. Although HDM and CDM both have the Zel'dovich spectrum shape (P(k) k) in the long-wavelength limit, because of the free-streaming cutoff the amplitude of the HDM spectrum must be considerably higher in order to form any structure by the present. With the COBE normalization, the HDM spectrum is only beginning to reach nonlinearity at the present epoch.

Thus the evidence against standard hot DM is convincing. At very least, it indicates that structure formation in a neutrino-dominated universe must be rather more complicated than in the standard inflationary picture.

The main alternative that has been considered is cosmic strings plus hot dark matter. Because the strings would continue to seed structure up until the present, and because these seeds are in the nature of rather localized fluctuations, hot DM would probably work better with string seeds than cold DM. However, strings and other cosmic defect models are now essentially ruled out [56, 57] because they predict that the cosmic microwave background would have an angular power spectrum without the pronounced (doppler/acoustic/Sakharov) peak at angular wavenumber l ~ 220 that now appears to be clearly indicated by the data, along with secondary peaks at higher l.