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8. PRECISION COSMOLOGY

The COBE DMR measurement of CMB anisotropy on the 10° angular scale and determination of the primeval deuterium abundance served to mark the beginning of a new era of precision cosmology. Overnight, COBE changed the study of large-scale structure: for theories like inflation and defects which specify the shape of the spectrum of density perturbations, the COBE measurement fixed the level of inhomogeneity on all scales to an accuracy of around 10%. Likewise, the measurement of the primeval deuterium abundance, led to a 10% determination of the baryon density.

Within the next few years, an avalanche of data, driven by advances in technology, promises definitive independent observations of the geometry, mass distribution and composition, and detailed structure of the Universe. In a radical departure from its history, cosmology is becoming an exact science. These new observations span the wavelength range from microwave to gamma rays and beyond, and utilize techniques as varied as CMB microwave interferometry, faint supernova photometry and spectroscopy, gravitational lensing, and massive photometric and spectroscopic surveys of millions of galaxies.

The COBE measurement of CMB anisotropy on angular scales from around 10° to 100° yielded a precise determination of the amplitude of mass fluctuations on very large scales, 103 Mpc-104 Mpc. A host of experiments will view the CMB with much higher angular resolution and more precision than COBE, culminating in the two satellite experiments, NASA's MAP and ESA's Planck Surveyor, which will map the full sky to an angular resolution of 0.1°. In so doing, the mass distribution in the Universe at a simpler time, before nonlinear structures had formed, will be determined on scales from 104 Mpc down to 10 Mpc. (Temperature fluctuations on angular scale theta arise from density fluctuations on length scales L ~ 100h-1 Mpc [theta / deg]; fluctuations on scales ~ 1 Mpc give rise to galaxies, on scales ~ 10 Mpc give rise to clusters, and on scales ~ 100 Mpc give rise to great walls.)

The multipole power spectrum of CMB temperature fluctuations has a rich structure and encodes a wealth of information about the Universe. The peaks in the power spectrum are caused by baryon-photon oscillations, which are driven by the gravitational force of the dark matter. Since decoupling is essentially instantaneous, different Fourier modes are caught at different phases, which is reflected in a multipole spectrum of anisotropy (see Fig. 5). The existence of the first peak is evident. If the satellite missions are as successful as cosmologists hope, and if foregrounds (e.g., diffuse emission from our own galaxy and extragalactic point sources) are not a serious problem, it should be possible to use the measured multipole power spectrum to determine Omega0 and many other cosmological parameters (e.g., OmegaBh2, h, n, level of gravitational waves, OmegaLambda, and Omeganu) to precision of 1% or better in some cases (see Wilkinson 1999).

Another impressive map is in the works. The present 3-dimensional structure of the local Universe will also be mapped to unprecedented precision in the next few years by the Sloan Digital Sky Survey (SDSS) (see Gunn et al. 1998), which will obtain the redshifts of a million galaxies over 25% of the northern sky out to redshift z ~ 0.1, and the Two-degree Field Survey (2dF), which will collect 250,000 redshifts in many 2° patches of the southern sky (Colless 1988). These surveys will cover around 0.1% of the observable Universe, and more importantly, will map structure out to scales of about 500h-1 Mpc, well beyond the size of the largest structures known. This should be large enough to provide a typical sample of the Universe. The two maps - CMB snapshot of the Universe at 300,000 yrs and the SDSS map of the Universe today - when used together have enormous leverage to test cosmological models and determine cosmological parameters.

Several projects are underway to map smaller, more distant parts of the Universe to study the ``recent'' evolution of galaxies and structure. Using a new large spectrograph, the 10-meter Keck telescope will begin to map galaxies in smaller fields on the sky out to redshifts of 4 or so. Ultimately, the Next Generation Space Telescope, which is likely to have an 8-meter mirror and capability in the infrared (most of the light of high-redshift galaxies has been shifted into the infrared) will probe the first generation of stars and galaxies.

Much of our current understanding of the Universe is based on the assumption that light traces mass, because telescopes detect light and not mass. There is some evidence that light is not a terribly ``biased'' tracer of mass, at least on the scales of galaxies. However, it would be a convenient accident if the mass-to-light ratio were universal. It is possible that there is a lot of undiscovered matter, perhaps even enough to bring OmegaM to unity, associated with dim galaxies or other mass concentrations that are not correlated with bright galaxies.

Gravitational lensing is a powerful means of measuring cosmic mass overdensities in the linear regime directly (see e.g., Blandford & Narayan 1992; Tyson 1993): dark matter overdensities at moderate redshift (z ~ 0.2-0.5) systematically distort background galaxy images (referred to as weak gravitational lensing). A typical random one-square-degree patch of the sky contains a million faint high-redshift galaxies. Using these galaxies, weak gravitational lensing may be used to map the intervening dark matter overdensities directly. This technique has been used to map known or suspected mass concentrations in clusters of galaxies over redshifts 0.1 < z < 0.8 (see Fig. 8 and Clowe et al. 1998) and only recently has been applied to random fields. Large mosaics of CCDs make this kind of direct mass survey possible, and results from these surveys are expected in the coming years.

Crucial to taking advantage of the advances in our understanding of the distribution of matter in the Universe and the formation of galaxies are the numerical simulations that link theory with observation. Simulations now involve billions of particles, allowing a dynamical range of a factor of one thousand (see Fig. 12). Many simulations now involve not only gravity, but the hydrodynamics of the baryons. Advances in computing have been crucial.

Figure 12

Figure 12. One of the largest simulations of the development of structure in the Universe. (from Virgo Collaboration 1998). Shown here is projected mass in a Lambda CDM simulation with 2563 particles and OmegaM = 0.3, 240 h-1 Mpc on a side. The map shown in Fig. 8 would correspond to a window 0.5 Mpc across, centered on one of the minor mass concentrations.

Impressive progress has been made toward measuring the cosmological parameters H0, q0 and t0, and more progress is on the horizon. A 5% or better measurement of the Hubble constant on scales that are a substantial fraction of the distance across the Universe may be within our grasp. Techniques that do not rely upon phenomenological standard candles are beginning to play an important role. The time delay of a flare event seen in the multiple images of a lensed quasar is related only to the redshifts of the lens and quasar, the lens magnification, the angular separation of the quasar images, and the Hubble constant. Thanks to a recent flare, an accurate time delay between the two images of the gravitationally lensed quasar Q0957+561 has been reliably determined, but the lens itself must be mapped before H0 is precisely determined (Kundic et al. 1997). This technique is being applied to other lensed quasar systems as well. The pattern of CMB anisotropy has great potential to accurately determine H0. Another technique (Sunyaev-Zel'dovich, or SZ), which uses the small distortion of the CMB when viewed through a cluster containing hot gas (due to Compton up-scattering of CMB photons), has begun to produce reliable numbers (Birkinshaw 1998).

Currently, the largest gap in our knowledge of the mass content of the Universe is identifying the bulk of the matter density, Omega? = OmegaM - OmegaB ~ 0.3. The most compelling idea is that this component consists of relic elementary particles, such as neutralinos, axions or neutrinos. If such particles compose most of the dark matter, then they should account for most of the dark matter in the halo of our own galaxy and have a local mass density of around 10-24 g cm-3. Several laboratory experiments are currently running with sufficient sensitivity to search directly for neutralinos of mass 10 GeV - 500 GeV and cross-section that is motivated by the minimal supersymmetric standard model. While the supersymmetric parameter space spans more than 3 orders-of-magnitude in cross section, even greater sensitivities are expected in the near future. These experiments involve high-sensitivity, low-background detectors designed to detect the small (order keV) recoil energy when a neutralino elastically scatters off a nucleus in the detector; the small rates (less than one scattering per day per kg of detector) add to the challenge (Sadoulet 1999).

An axion detector has achieved sufficient sensitivity to detect halo axions, and is searching the mass range 10-6 eV - 10-5 eV where axions would contribute significantly to the mass density. This detector, based upon the conversion of axions to photons in strong magnetic field, consists of a hi-Q cavity immersed in a 7 Tesla magnetic field and is operating with a sensitivity of 10-23 W in the GHz frequency range. Within five years it is hoped that the entire theoretically favored mass range will be explored (Rosenberg 1998).

While light neutrinos are no longer favored by cosmologists for the dark matter, as they would lead to structure in the Universe that is not consistent with what we see today, because of their large numbers, 113 cm-3, they could be an important component of mass density even if only one species has a tiny mass:

Equation 11a
Equation 11b
Equation 11c (11)

Even with a mass as small as one eV neutrinos would make an imprint on the structure of the Universe that is potentially detectable.

Particle theorists strongly favor the idea that neutrinos have small, but nonzero mass, and the see-saw mechanism can explain why their masses are so much smaller than the other quarks and leptons: mnu ~ m2q, l / M where M ~ 1010 GeV - 1015 GeV is the very large mass of the right-handed partner(s) of the usual left-handed neutrinos (see e.g., Schwarz & Seiberg 1999). Because neutrino masses are a fundamental prediction of unified field theories, much effort is directed at probing neutrino masses. The majority of experiments now involve looking for the oscillation of one neutrino species into another, which is only possible if neutrinos have mass. These experiments are carried out at accelerators, at nuclear reactors, and in large-underground detectors such as Super-Kamiokande and the SNO facility.

Super-K detects neutrinos from the sun and those produced in the earth's atmosphere by cosmic-ray interactions. For several years now the solar-neutrino data has shown evidence for neutrino oscillations, corresponding to a neutrino mass-difference squared of around 10-5 eV2 or 10-10 eV2, too small to be of cosmological interest (unless two neutrino species are nearly degenerate in mass.) The Super-K collaboration recently announced evidence for neutrino oscillations based upon the atmospheric neutrino data. Their results, which indicate a mass-difference squared of around 10-3-10-2 eV2 (Fukuda et al. 1998) and imply at least one neutrino has a mass of order 0.1 eV or larger, are much more interesting cosmologically. Over the next decade particle physicists will pursue neutrino mass with a host of new experiments, characterized by very long baselines (neutrino source and detector separated by hundreds of kilometers) and should clarify the situation.

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