Hot Gas in Clusters. Hot gas has been found in clusters of galaxies by the German satellite ROSAT and the Japanese satellite ASCA. The temperature of the gas can be used to estimate the gravitational potential of the clusters if it is assumed that the gas is vivialized and purely supported by thermal pressure. Similarly, the intensity of the emission can be used to estimate the density of the gas. White et al. (66) have shown that the typical values for x-ray clusters yield a hot gas to total mass ratio MHOT/MTOT of about 0.2. If clusters are representative of the universe as they would be in standard cold dark matter models, and if ΩTOTAL=1, then MHOT/MTOTb. Even with the spread in MHOT/MTOT in clusters as found by Mushotsky (67), only a marginal overlap is at very low H0 and the high end of Ωb from BBN. Clearly, higher values of ΩBBN are favored by this argument. However, it should be noted that various systematic effects such as: magnetic field pressure in clusters (68), clumping of the hot gas regions, and admixture of hot dark matter (69) all go in the direction of increasing MTOTAL and improving the overlap. Also, if clusters are not fair samples of the universe, then concordance is not needed here. This latter point may be implied by the variations observed by Mushotsky (67), because, if clusters are fair samples, then they all should be giving the same answer. Another way to obtain concordance is if ΩTOTAL<1! All of these caveats tell us that clusters do not represent any “baryon catastrophe,” but they are important to continue to monitor, and it is clear that the overlap is better for higher ΩBBN and requires less variation from the standard assumptions. Regardless of Ωb implied by x-ray gas, the total cluster mass implied is consistent with that implied by dynamics and lensing.

Microwave Anisotropies. The method with the most potential for checking Ωb is the measurement of the acoustic peaks in the microwave background anisotropy at angular scales near 1° or less (7072). The height of the first doppler (acoustic) peak for gaussian fluctuation models is directly related to ΩBh2, thus a direct check on BBN. Current experiments at the South Pole and at Sasketoon, and by using balloons seem to favor values near the high side of the BBN range, but the present uncertainties are too large to make any strong statements. However, the next generation of satellites, the National Aeronautics and Space Administration’s MAP and the European Space Agency’s PLANCK (formerly COBRAS/ SAMBA) should be able to fix Ωbh2 to better than 10% (if the sky is gaussian), which should provide a dramatic test of BBN.

Dark Matter

The robustness of the basic BBN arguments and the new D/H measurements have given renewed confidence to the limits on the baryon density constraints. Let us convert this density regime into units of the critical cosmological density for the allowed range of Hubble expansion rates. This is shown in Fig. 2. Fig. 2 also shows the lower bound on the age of the universe of 10 Gyr from both nucleochronology and from globular cluster dating (32) and a lower bound on H0 of 38 from extreme type IA supernova models with pure 1.4 M carbon white dwarfs being converted to 56Fe. The constraint on Ωb means that the universe cannot be closed with baryonic matter. [This point was made over 20 yr ago (73) and has proven to be remarkably strong.] If the universe is truly at its critical density, then nonbaryonic matter is required. This argument has led to one of the major areas of research at the particle-cosmology interface, namely, the search for nonbaryonic dark matter. In fact, from the lower bound on ΩTOTAL from cluster dynamics of ΩTOTAL>0.1, it is clear that nonbaryonic dark matter is required unless H0<40. The need for nonbaryonic matter is strengthened on even larger scales (74). Fig. 2 also shows the range of ΩVISIBLE and shows no overlap is between Ωb and ΩVISIBLE. Hence, the bulk of the baryons are dark.

Another interesting conclusion (32) regarding the allowed range in baryon density is that it is in agreement with the density implied from the dynamics of single galaxies, including their dark halos. The recent Massive Compact Halo Object (MACHO) (75) and Earth Resources Observation Satellite (EROS) (76) reports of halo microlensing may well indicate that at least some of the dark baryons are in the form of brown dwarfs in the halo. However, Gates, Gyuk, and Turner (77) and Alcock et al. (75, 78) show that the observed distribution of MACHOs favors less than 50% of the halo being in the form of MACHOs, but a 100% MACHO halo cannot be completely excluded yet.

For dynamical estimates of Ω, one estimates the mass from where v is the relative velocity of the objects being studied, r is their separation distance, and G is Newton’s constant. The proportionality constant out front depends on orientation, relative mass, etc. For large systems such as clusters, one uses averaged quantities. For single galaxies v would represent the rotational velocity and r the radius of the star or gas cloud. It is this technique that yields the cluster bound on Ω shown in Fig. 2. It should be noted that the value of ΩCLUSTER~0.25 also is obtained in those few cases where alignment produces giant gravitational-lens arcs. Recent work using weak gravitational lensing by Kaiser (79) also supports large Ω. As Davis (74) showed, if the large-scale velocity flows measured from the IRAS satellite survey are due to gravity, then ΩIRAS≳0.2. For H0>40, ΩCLUSTER already requires ΩTOTALBARYON and hence the need for nonbaryonic dark matter.

An Ω of unity is, of course, preferred on theoretical grounds because that is the only long-lived natural value for Ω, and inflation (80, 81) or something like it provided the early universe with the mechanism to achieve that value and thereby solve the flatness and smoothness problems. Note that our need for exotica is not dependent on the existence of dark galatic halos and that high values of H0 increase the need for nonbaryonic dark matter.

It also is interesting to note that the convergence of Ω on cluster scales at ~0.25±0.1 has important implications. If ΩTOTAL is really unity, it would necessitate clusters not being a fair sample of the universe. Because standard cold dark matter implies cluster scales as fair samples, this would imply a more complex structure formation picture. Options include biasing on cluster scales, a very hot dark matter component, or even a smooth background component such as a Λ0 term, or a vacuum energy from a late-time phase transition (82, 83).

I would like to thank my collaborators, Craig Copi, Ken Nollett. Martin Lemoine, David Dearborn, Brian Fields, Dave Thomas, Gary Steigman. Brad Meyer, Keith Olive. Angela Olinto, Bob Rosner, Michael Turner, George Fuller, Karsten Jedamzik, Rocky Kolb, Grant Mathews. Bob Rood, Jim Truran, and Terry Walker for many useful discussions. I would further like to thank Art Davidsen. Poul Nissen. Jeff Linsky, David letter, Len Cowie, Craig Hogan, Julie Thorburn, Doug Duncan, Lew Hobbs, Evan Skillman, Bernard Pagel, and Don York for valuable discussion regarding the astronomical observations. This work is supported by the National Aeronautics and Space Administration (NASA) and the Department of Energy (nuclear) at the University of Chicago, and by the Department of Energy and NASA Grant NAG5–2788 at Fermilab.

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