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2. 1998 - A Most Memorable Year for Cosmology

1998 saw the first plausible, complete accounting of matter and energy in the Universe; a precision determination of the density of ordinary matter; and other strong evidence supporting the basic tenets of Inflation + Cold Dark Matter (CDM). If subsequent data and observations confirm and strengthen the case, I believe we will ultimately refer to 1998 as a turning point in cosmology as important as 1964.

As discussed by Silk, the small variations in the CMB temperature across the sky have the potential to determine the geometry of the Universe and thereby Omega0, the fraction of critical density contributed by all forms of matter and energy. [Note, the curvature radius of the Universe and Omega0 are related by, R2curv = H0-2 / |Omega - 1|, so that Omega = 1 corresponds to a flat geometry, Omega < 1 corresponds to negatively curved (open) geometry, and Omega > 1 corresponds to positively curved (closed) geometry.] In a flat Universe the differences in temperature between points on the sky are greatest when the two points are separated by about one degree; in an open Universe, they are greatest when the separation is smaller than one degree. The data that now exist indicate that the differences are indeed greatest on the one-degree scale (see Fig. 1). More measurements are being made - from balloons, in Antarctica, and on the Atacama Plateau in Chile - with definitive measurements to come from two new satellites: NASA's MAP (launch 2000) and ESA's Planck Surveyor (launch (2007). If the trend in the results continues, then we have determined that the Universe is spatially flat and Omega = 1.

Figure 1

Figure 1. Summary of all CMB anisotropy measurements, where the CMB temperature variation across the sky has been expanded in spherical harmonics, delta T(theta , phi ) = Sigmai alm Ylm and Cl ident < |alm|2 >. In simple language, this plot shows the size of the temperature variations between two points on the sky separated by angle theta (ordinate) vs. multipole number l = 200° / theta (l = 2 corresponds to 100°, l = 200 corresponds to theta = 1°, and so on). The curves illustrate the predictions of CDM models with Omega0 = 1 (curve with lower peak) and Omega0 = 0.3 (darker curve). Note: the preference of the data for a flat Universe, and the evidence for the first of a series of ``acoustic peaks.'' The presence of these acoustic peaks is a key signature of the density perturbations of quantum origin predicted by inflation (Figure courtesy of M. Tegmark).

These same measurements of the temperature variations of the CMB temperature across the sky also provide important information about the matter inhomogeneities that seeded all the structure we see in the Universe today. Recall, that as Silk explained, the pattern of hot and cold spots on the microwave sky arises due to the lumpy distribution of matter, and in this way the CMB is a snapshot of the Universe at 300,000 years after the beginning (CMB photons come directly to us from their last scattering at this time). The first mapping of the distribution of matter in early Universe using the CMB was done by NASA's COBE satellite (Smoot et al. 1992); since then, many other experiments, with better angular resolution, have ``enhanced the picture.'' At present, the pattern of hot and cold spots indicate, though do not yet prove, that the primeval lumpiness had the following characteristics: Gaussian fluctuations in the curvature of the Universe with an approximately scale-invariant spectrum (see Fig. 1). This is precisely what inflation predicts.

Of the four light elements made in the big bang, the yield of deuterium is most sensitive to the density of ordinary matter (baryons), and for that reason David Schramm and I nicknamed it ``the baryometer'' (Schramm & Turner 1998). Deuterium is also ``very fragile,'' easily destroyed by nuclear reactions in stars. The abundance of deuterium in our local neighborhood has been known for more than twenty years, but because about half of the material around us has been through stars, we cannot interpret the locally measured abundance as the primordial, big-bang abundance. This year, David Tytler and Scott Burles (Burles & Tytler 1998a, b) measured the deuterium abundance in very distant hydrogen clouds. Because these clouds are so distant, we are seeing them at an early time, before stars have destroyed their deuterium. Their measurement of the primeval deuterium abundance pegs the contribution of ordinary matter to be 5% of the critical density (for a Hubble constant of 65 km s-1 Mpc-1), with a precision of better than ± 0.5% (see Fig. 2).

Figure 2

Figure 2. Predicted abundances of 4He, D, 3He, and 7Li (relative to hydrogen) as a function of the density of ordinary matter (baryons). The full band denotes the concordance interval based upon all four light elements that dates back to 1995. The darker portion highlights the determination of the density of ordinary matter based upon the recent measurement of the primordial abundance of deuterium (Burles & Tytler 1998a, b), which implies that ordinary matter contributes 5% of the critical density.

In addition to pinning down the amount of ordinary matter, the Tytler - Burles measurement has allowed us to determine the total amount of matter, using a very clever technique pioneered by Simon White and his colleagues (White et al 1993). They argue that clusters of galaxies, by virtue of their large size (tens of millions of light years in size and thousands of galaxies in number), represent a fair sample of matter in the Universe. Thus, the ratio of baryons to matter in clusters, together with the big-bang determination of the average density of baryons in the Universe serve to pin down the average matter density in the Universe:

Equation 1
Equation 2 (1)

Most of the baryons in clusters exist in the form of hot, x-ray emitting gas and the intensity of x-ray emission allows a determination of the amount of ordinary matter. The total cluster mass can be determined in a number of ways: by direct mapping of the mass by gravitational lensing, by measuring the x-ray temperature, and by measuring the random motion of galaxies; all three give the same answer. The ratio of baryons to matter has been determined to be 13% ± 1.5%. This implies that matter contributes 40% ± 10% of the critical density. (Other determinations of the matter density indicate a similar value.)

The determination that matter contributes 40% of the critical density has two implications. First, as Silk discussed, most of the matter in the Universe is not the stuff we are made out of, which follows from the inequality, OmegaMatter > OmegaBaryon. That is, the matter that provides the cosmic infrastructure and holds the Universe together is something exotic (or, perhaps we should say that we are made of something more exotic). That is a remarkable fact. As I will discuss, the most promising idea is that this exotic matter is relic elementary particles left over from the earliest moments of creation.

The second, equally profound implication follows from the inequality, Omega > OmegaMatter. This implies the existence of a form of matter or energy that does not clump (as evidenced by the fact that it is not found in clusters) and yet contributes 60% of the critical density. The fact that this funny component to the energy density does not clump and contributes so much of the critical density implies that it must be very elastic (the technical term is negative pressure) and leads to a striking prediction: that the expansion of the Universe should be speeding up, rather than slowing down!

This requires further explanation: According to Einstein's theory of general relativity, the source of gravity is energy density + three times the pressure (Note: matter and energy are equivalent, related by E = mc2; Newton's theory of gravity holds that the source of gravity is matter alone.) If the pressure is sufficiently negative - and it must be if the additional component is to remain smooth - its gravity is repulsive! Because there is so much of this ``funny'' energy, the net effect of gravity on the expansion of the Universe is repulsive and so the Universe should be speeding up, rather than slowing down! Sandage's famous deceleration parameter embodies all of this, q0 = (Omega / 2) [1 + 3p/rho] is negative if p < -rho / 3.

(An aside: the fact that energy density + three times pressure is the source of gravity in Einstein's theory also leads to the prediction of black holes. An object with very strong gravity needs great pressure to balance gravity; objects with stronger and stronger gravity - i.e., stars of greater and greater mass - need more and more pressure; eventually, the pressure becomes counterproductive, producing more gravity, resulting in a black hole.)

The prediction of accelerated expansion was confirmed in 1998 and completed the accounting of matter and energy in the Universe. By studying the relationship between the distances and velocities of distant galaxies by using exploding stars (supernovae of type Ia, or SNeIa) within them as standard candles, two teams (the Supernova Cosmology Project led by Saul Perlmutter and the High-redshift Search Team led by Brian Schmidt) found evidence that the Universe is speeding up, rather than slowing down (Perlmutter et al. 1998; Riess et al. 1998). Let me explain their results by telling you what they expected to find and what they actually did find. Because the expansion of the Universe is simply a scaling up of all distances, if we could measure galaxy velocities and positions today, they would obey exactly Hubble's law: recessional velocity proportional to distance (v = H0 d). However, as we look far out into space, we look back in time (light travels at a finite speed), and so we are viewing distant galaxies at earlier and earlier times. If the Universe is slowing down, distant galaxies should be moving faster than Hubble's law predicts. These two groups found the opposite: distant galaxies are moving more slowly than Hubble's law predicts. The expansion is speeding up.

The simplest interpretation of their results is that vacuum energy, with pressure equal to minus its energy density, contributes about 60% of the critical density, making consistent the determinations Omega =1 and OmegaMatter = 0.4. Vacuum energy is the modern term we use for Einstein's cosmological constant. It corresponds to the energy associated with the very lively quantum vacuum - pairs of particles borrowing enough energy to exist for a fleeting instant and then disappearing again.

To summarize the accounting of matter and energy in the Universe (in units of the critical density): neutrinos, 0.3% or greater; bright stars, 0.5%; total amount of ordinary matter (baryons), 5%; relic elementary particles, 35%; and vacuum energy (or something similar), 60%; for a total of 100% of the critical density (see Fig. 3). While this accounting is not definitive yet, measurements that are being made and will be made in the next years could firm it up.

Figure 3

Figure 3. 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 of structure formation and the lower limit follows from the evidence for neutrino oscillations (Fukuda et al. 1998). Here H0 is taken to be 65 km s-1 Mpc-1.

(Only about one-tenth of the baryons are ``visible'' in the form of bright stars. Further, because there are almost as many neutrinos left over from the big bang as there are CMB photons and because evidence now exists that at least two of the neutrino species have mass, albeit very tiny (Fukuda et al. 1998), we can infer that neutrinos contribute as much mass, and perhaps even more, than stars do. However, both neutrinos and bright stars are small contributors to the total mass in the Universe.)

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