5.1 Dark Matter and Dark Energy

Our knowledge of the mass and energy content of the Universe is still poor, but is improving rapidly (see Sadoulet 1999). We can confidently say that most of the matter in the Universe is of unknown form and dark (see e.g., Dekel et al. 1997; Bahcall et al. 1993): Stars (and closely related material) contribute a tiny fraction of the critical density, _lum = (0.003 ± 0.001) h^-1 0.004, while the amount of matter known to be present from its gravitational effects contributes around ten times this amount, _M = 0.35 ± 0.07 (this error flag is ours; it is meant to indicate 95% certainty that _M is between 0.2 and 0.5). The gravity of dark matter is needed to hold together just about everything in the Universe - galaxies, clusters of galaxies, superclusters and the Universe itself. A variety of methods for determining the amount of matter all seem to converge on _M ~ 1/3; they include measurements of the masses of clusters of galaxies and the peculiar motions of galaxies. Finally, the theory of big-bang nucleosynthesis and the recently measured primeval abundance of deuterium pin down the baryon density very precisely: _B = (0.02 ± 0.002) h^-2 0.05. The discrepancy between this number and dynamical measurements of the matter density is evidence for nonbaryonic dark matter.

Particle physics suggests three dark matter candidates (Sadoulet 1999): a 10^-5 eV axion (Rosenberg 1998); a 10 Gev - 500 Gev neutralino (Jungman, Kamionkowski, and Griest 1996); and a 30 eV neutrino. These three possibilities are highly motivated in two important senses: first, the axion and neutralino are predictions of fundamental theories that attempt to go beyond the standard model of particle physics, as are neutrino masses; and second, the relic abundances of the axion and neutralino turn out to be within a factor of ten of the critical density - and similarly for the neutrino, GUTs predict masses in the eV range, which is what is required to make neutrinos a significant contributor to the mass density.

Because measuring the masses of galaxy clusters has been key to defining the dark matter problems it is perhaps worth further discussion. Cluster masses can be estimated by three different techniques - which give consistent results. The first, which dates back to Fritz Zwicky (1935), uses the measured velocities of cluster galaxies and the virial theorem to determine the total mass (i.e., KE_gal |PE_gal|/2). The second method uses the temperature of the hot x-ray emitting intracluster gas and the virial theorem to arrive at the total mass. The third and most direct method is using the gravitational lensing effects of the cluster on much more distant galaxies. Close to the cluster center, lensing is strong enough to produce multiple images; farther out, lensing distorts the shape of distant galaxies. The lensing method allows the cluster (surface) mass density to be mapped directly. An example of mapping the mass distribution of a cluster of galaxies is shown in Fig. 8.

Figure 8. The reconstructed total mass density in the cluster of galaxies 0024+1654 at redshift z = 0.39, based on parametric inversion of the associated gravitational lens. Projected mass contours are spaced by 430 M pc-2, with the outer contour at 1460 M pc-2. Excluding dark mass concentrations centered on visible galaxies, more than 98% of the remaining mass is represented by a smooth concentration of dark matter centered near the brightest cluster galaxies, with a 50 kpc soft core (Tyson et al. 1998).

Using clusters to estimate the mean mass density of the Universe requires a further assumption: that their mass-to-light ratio provides a good estimate for the mean mass-to-light ratio. This is because the mean mass density is determined by multiplying the mean luminosity density (which is reasonably well measured) by the inferred cluster mass-to-light ratio. Using this technique, Carlberg et al. (1996, 1997) find _M = 0.19 ± 0.06 ± 0.04. If clusters have more luminosity per mass than average, this technique would underestimate _M.

There is another way to estimate _M using clusters, based on a different, more physically motivated assumption. X-ray measurements more easily determine the amount of hot, intracluster gas; and as it turns out, most the baryonic mass in a cluster resides here rather than in the mass of individual galaxies (this fact is also confirmed by lensing measurements). Together with the total cluster mass, the ratio of baryonic mass to total mass can be determined; a compilation of the existing data give M_B / M_TOT = (0.07 ± 0.007) h^-3/2 0.15 (Evrard 1997 and references therein). Assuming that clusters provide a fair sample of matter in the Universe so that _B / _M = M_B / M_TOT, the accurate BBN determination of _B can be used to infer: _M = (0.3 ± 0.05) h^-1/2 0.4. [A similar result for the cluster gas to total mass ratio is derived from cluster gas measurements based upon the distortion of the CMB spectrum due to CMB photons scattering off the hot cluster gas (Sunyaev - Zel'dovich effect); see Carlstrom 1999.]

Two other measurements bear on the quantity and composition of energy and matter in the Universe. First, the pattern of anisotropy in the CMB depends upon the total energy density in the Universe (i.e., ₀) (see e.g., Jungman, Kamionkowski, Kosowsky and Spergel 1996). The peak in the multipole power spectrum is l_peak 200 / sqrt(₀). The current data, shown in Fig. 5, are consistent with ₀ 1, though ₀ ~ 0.3 cannot be excluded. This together with the evidence that _M 0.3 leaves room for a component of energy that does not clump, such as a cosmological constant.

The oldest approach to determining the total mass-energy density is through the deceleration parameter (Baum 1957; Sandage 1961), which quantifies the present slowing of the expansion due to gravity,

(9)

where subscript zero refers to quantities measured at the current epoch. Note, in a Universe where the bulk of the matter is nonrelativistic (p ), q₀ and ₀ differ only by a factor of two. The luminosity distance to an object at redshift z << 1 is related to q₀,

(10)

and thus accurate distance measurements can be used to determine q₀. (The luminosity distance to an object is defined as that inferred from the inverse square law: d_L sqrt( / 4 .)

Recently, two groups (The Supernova Cosmology Project and The High-z Supernova Team) using Type Ia supernovae (SNe1a) as standard candles (objects of known ) and assuming that their flux measurements (i.e., ) were not contaminated by sample selection, evolution, or dust systematics, both conclude that the expansion of the Universe is accelerating rather than decelerating (i.e., q₀ < 0) (Perlmutter et al. 1998; Schmidt et al. 1998). If correct, this implies that much of the energy in the Universe is in an unknown component, with negative pressure, p_X -_X / 3 (Garnavich et al. 1998). The simplest explanation is a cosmological constant with ~ 2/3. (In fact, Equ. 10, which is deeply rooted in the history of cosmology, is not sufficiently accurate at the redshifts of the SNe1a being used, and the two groups compute d_L (1 + z)r(z) as a function of _M and and fit to the observations.)

Pulling this together, cosmologists for the first time have a plausible accounting of matter and energy in the Universe: stars contribute around 0.4% of the critical density, baryons contribute 5%, nonrelativistic particles of unknown type contribute 30%, and vacuum energy contributes 64%, for a total equaling the critical density (see Figures 9 and 10). We should emphasize that plausible does not mean correct.

Figure 9. Constraints in the vs M plane. Three different types of observations are shown: SNe Ia measures of expansion acceleration (SN); the CMB observations of the location of the first acoustic peak (CMB); and the determinations of the matter density, M = 0.35 ± 0.07 (dark vertical band). The diagonal line indicates a flat Universe, M + = 1; regions denote "3-" confidence. Darkest region denotes the concordance region: ~ 2/3 and M ~ 1/3.

Figure 10. Summary of matter/energy in the Universe. The right side refers to an overall accounting of matter and energy; the left refers to the composition of the matter component. The upper limit to mass density contributed by neutrinos is based upon the failure of the hot dark matter model and the lower limit follows from the SuperK evidence for neutrino oscillations. Dark Energy range is preliminary.

Experimental searches for dark stars in our own galaxy have been carried out using the gravitational microlensing technique: dark stars along the line of sight to nearby galaxies (e.g., the Large and Small Magellanic Clouds and Andromeda) can gravitationally lens the distant bright stars, causing a well-defined temporary brightening (Paczynski 1986). The results, however, are perplexing (see e.g., Sadoulet 1999). More than a dozen such brightenings of LMC stars have been seen, suggesting that a significant fraction of our galaxy's halo exists in the form of half-solar mass white dwarfs. However, such a population of white dwarfs should be visible, and they have not been seen. Because of our imperfect knowledge of our own galaxy and the LMC, it is possible that the lenses are not associated with the halo of our galaxy but rather are low-mass stars in the LMC, in an intervening dwarf galaxy in between, or are actually in the disk of our galaxy, if the disk is warped enough to pass in front of the line to the LMC.