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2.2. The Expansion of the Universe

The expansion of the universe was discovered in 1929 by Edwin Hubble, who measured the distances to a sample of nearby galaxies, and established a correlation between distance and recession velocity. The slope of this relation is the Hubble constant. Large systematic uncertainties in determining distance have made an accurate determination of the Hubble constant a challenge, and only recently have improvements in instrumentation, the launch of the Hubble Space Telescope (HST), and the development of several different measurement methods led to a convergence on its value. Accurate distances to nearby galaxies obtained as part of an HST Key Project have allowed calibration of 5 different methods for determining the distances to galaxies out to 500 Mpc (Freedman et al., 2001). All the techniques show good agreement to within their respective uncertainties, and yield a value


where the error bars represent 1-sigma statistical and systematic uncertainties, respectively (see Figure 3). Because of the importance of its value to so many cosmological quantities, and because of its historically large uncertainty, H0 is often written as H0 = 100h km sec-1 Mpc-1, so that h = 0.72 ± 0.02 ± 0.07.

Figure 3

Figure 3. Hubble diagram: Low-redshift galaxies are used to establish the expansion of the Universe and the Hubble constant; the consistency of the five different distance indicators is shown. The lower panel shows the value of the Hubble constant object by object and the convergence to 72km/s/Mpc. The scatter at distances less than 100Mpc arises due to gravitational induced "peculiar velocities" that arise from the inhomogeneous distribution of matter.

The largest contributions to these quoted uncertainties result from those due to the metallicity of Cepheids, the distance to the Large Magellanic Cloud (the fiducial nearby galaxy to which all Cepheid distances are measured relative to), and the calibration of the Wide Field Camera on HST. Other groups using similar techniques (Saha et al., 1997) find a lower value of H0 (~ 60 km/sec/Mpc). The reasons for the difference are many, as described further in Freedman et al. (2001), but overall the determinations are consistent to within the measurement uncertainties. Recent measurements of H0 based on two completely independent techniques, the Sunyaev-Zeldovich method and the measurement of time delays for gravitational lenses (Reese et al., 2000, Keeton et al., 2000), are yielding values of H0 ~ 60 km/sec/Mpc with systematic errors currently still at the 20-30% level. New results from the WMAP satellite, discussed in the postscript to this article, give H0 = 71 ± 4 km/sec/Mpc.

Because light from very distance galaxies was emitted long ago, the Hubble diagram also provides a means of probing the expansion at earlier times. For many decades, efforts have been directed toward measuring what was almost universally expected to be a slowing of the expansion over time due to the gravity of all the matter. However, observations by two independent groups have found that supernovae at high redshifts are fainter than predicted for a slowing expansion and indicate that the expansion is actually speeding up (see Figure 4) (Perlmutter et al., 1999, Riess et al., 1998). Although systematic effects due to intervening dust or evolution of the supernovae themselves could explain such a dimming of high-redshift supernovae, several tests have failed to turn up any evidence for such effects. Apparently, the universe is now undergoing an acceleration, with the repulsive gravity of some strange energy form - dark energy - at work. There is weak evidence in the supernova data for an earlier (z > 1/2), decelerating phase (Turner and Riess, 2002). Such a decelerating phase is expected on theoretical grounds (more later), and establishing its existence (or absence!) is an important goal of future supernova observations.

Figure 4

Figure 4. Hubble diagram: High-redshift type Ia supernovae probe the expansion history and reveal accelerated expansion. In this differential Hubble diagram the distance modulus, which is 5 times the logarithm of the distance, relative to an empty Universe (Omega0 = 0) is plotted. Measurements from more than 200 type Ia supernova are binned into 9 data points. The solid curves represent three theoretical models: from the top, OmegaLambda = 0.7 and OmegaM = 0.3; OmegaLambda = 0 and OmegaM = 0.3; and OmegaLambda = 0 and OmegaM = 1. The broken curve represents a nonaccelerating, flat Universe (i.e., q = 0 for all z); points above this curve indicate acceleration (adapted from data in Tonry et al., 2003).

The remarkable fact that the expansion is speeding up, rather than slowing down, can be accounted for within Einstein's theory, as the source of gravity is proportional to (rho + 3p), where the pressure p and energy density rho describe the bulk properties of the "substance". (For ordinary or even nonbaryonic dark matter, p = 0, while for photons and relativistic particles, p = rho / 3.) A substance that is very elastic, i.e., with pressure more negative than one third its energy density, has repulsive gravity in Einstein's theory (more later). Of course, it could well be that the root cause of cosmic acceleration is not new stuff (i.e., dark energy), but involves a deeper understanding of gravity.

The deceleration parameter was introduced to quantify the slowing of the expansion; it is related to the mass-energy content of the Universe:

Equation 3 (3)

where wX ident pX / rhoX characterizes the pressure of the dark-energy component. (wX need not be constant; for simplicity, we shall assume it is.) In the absence of dark energy, a flat Universe would decelerate by its own self-gravity (i.e., q0 = 0.5), whereas dark energy allows for acceleration. The supernova measurements are consistent with wX = - 1 and OmegaX = 0.7. Independent confirmation of such a startling result is extremely important. As discussed below, strong indirect evidence for an additional energy component comes from a comparison of the density of matter with measurements of Omega0 from fluctuations in the CMB.

Dark energy, a "mysterious substance" whose pressure is negative and comparable in magntiude to its energy density, apparently accounts for two-thirds of the matter-energy budget of the universe and has no clear explanation. Understanding its nature presents one of the greatest challenges in both cosmology and particle physics.

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