5.2.1. What Comes First - Galaxy-size or Cluster-size Potentials?

While the real Universe is likely some complex hybrid of HDM and CDM, we can consider three limiting cases of structure formation that arise under the gravitational instability paradigm. Each of these three cases assumes that a single kind of particle dominates the mass in the Universe.

The Top-down Scenario

Under this scenario, all fluctuations which are smaller than a horizon size are erased by the free streaming motion of relativistic particles. This scenario best applies in a HDM dominated universe in which the HDM particle is a neutrino. A convenient way to express the critical density in units of energy density is

where h = H₀ / 100. The conversion from h to m uses a neutrino density at z = 0 of 100 cm^-3. For h = 1 (H₀ = 100) = 1 requires m. For h = 1/2 (H₀ = 50) m 30 ev yields = 1. If, as suggested in Chapters 3 and 4, h 0.8 and m 2.5 eV then = 0.03.

The freestreaming of neutrinos stops when they become non-relativistic. This occurs through expansion and cooling of the Universe. When the universe has cooled to the point where kT is equal to the rest mass energy of the neutrino (m), they become non-relativistic. At this point the universe has some horizon size, r_hor, and variations in neutrino density can only occur on scales larger than r_hor. The total mass within the horizon is approximately

For m 30 eV, the horizon mass is 10¹⁶ M. This mass is similar to the mass of the putative Great Attractor discussed in the last chapter. For a neutrino dominated Universe, potentials of this mass would be the first to form. The formation of smaller scale structure would occur from fragmentation of gas within these potentials. This scenario then predicts that all smaller scale structures should be embedded in larger scale structures, which is in good qualitative agreement with the observations. The greatest strength of this scenario lies in its natural ability to produce power on large scales (e.g., superclusters). Its greatest weakness (see below) lies in the supreme difficulty of producing small scale structure early on in the Universe.

The Bottom-up Scenario

This is the scenario that Newton would have preferred as structure in the Universe is built by the hierarchical gravitational clustering of subunits. The minimum mass of these subunits is set by the Jeans instability criterion previously described. In a CDM dominated Universe, the hypothetical CDM particles are not subject to radiation drag in the early Universe and thus can begin to clump via gravitational instability at very early times (perhaps as early as the end of the inflationary epoch). Amplification of these seeds will then produce density fluctuations which can acrete baryonic material after recombination. As this material continues to flow into the density fluctuation, it continues to grow in size thus sweeping up more material in the vicinity. Eventually galaxy size objects are made via this gravitational coalescence of subunits and then clusters of galaxies are made later in the Universe via the continuation of this gravitational clustering hierarchy.

The greatest strength of the CDM dominated scenario is the natural production of small scale structure that should be embedded in a large scale distribution of dark matter. Furthermore, galaxy formation is something that occurs early on. The greatest weakness of the CDM model lies in its inability to produce the truly large scale structure that is observed. An interesting consequence of the bottom-up scenario is the suggestion that their may be totally dark galaxies, that is, CDM dominated potentials which were unable to trap and confine baryonic gas that subsequently fragmented into stars to produce a luminous galaxy to mark the location of that potential. In addition, the bottom-up scenario also predicts that cluster formation via gravitational merging of subunits is continuing at the present epoch. This would provide a natural source to generate the observed peculiar velocities. The detection of high redshift clusters would not be expected under this scenario.

The Baryon Dominated Scenario

This is a variant of the bottom-up scenario that would occur in a low Universe that is dominated by baryons. Of course, baryonic fluctuations can not easily grow during the radiation dominated error so the relevant issue is the amplitude of the Jeans length at the time of recombination. While it is quite unlikely that the Universe is baryon dominated, this scenario naturally produces old globular clusters whose formation is difficult to understand in the other two scenarios. But a particular problem with this scenario again is galaxy formation. Presumably, it would occur via the gravitational coalescence of globular cluster size objects. During this process tidal forces between globular clusters should liberate a lot of the more weakly bound stars. While this mechanism does produce a field population of old halo stars, observations of our own Galaxies as well as others shows that this halo of stars is extremely diffuse and fails, by two orders of magnitude, to contain enough mass to account for flat rotation curves. It also seems likely that the formation of galaxies via the gravitational clustering of Jeans mass density enhancements is not very efficient, and we would not expect to find many baryons in galaxies. Hence, a test of this scenario would involve determining the ratio of baryons that are in galaxies compared to those that are distributed in an intergalactic population. While there is some evidence for an intergalactic population of baryons (see chapter 6) it is fairly clear that there is not an order of magnitude more baryons outside of galactic potentials than inside of them.