3. FROM EINSTEIN TO ACCELERATED EXPANSION

Although the discovery of cosmic acceleration is often portrayed as a major surprise and a radical contravention of the conventional wisdom, it was anticipated by a number of developments in cosmology in the preceding decade. Moreover, this is not the first time that the cosmological constant has been proposed. Indeed, the cosmological constant was explored from the very beginnings of General Relativity and has been periodically invoked and subsequently cast aside several times since. Here we recount some of this complex 90-year history.

3.1. Greatest blunder?

Einstein introduced the cosmological constant in his field equations in order to obtain a static and finite cosmological solution "as required by the fact of the small velocities of the stars" and to be consistent with Mach's principle [ Einstein 1917]. In Einstein's solution, space is positively curved, R_curv = 1 / (4 G _M)^1/2, and the "repulsive gravity" of is balanced against the attractive gravity of matter, = _M/2. In the 1920's, Friedmann and Lemaître independently showed that cosmological solutions with matter and generally involved expansion or contraction, and Lemaître as well as Eddington showed that Einstein's static solution was unstable to expansion or contraction. In 1917, de Sitter explored a solution in which _M is negligible compared to [de Sitter 1917]. There was some early confusion about the interpretation of this model, but in the early 1920's, Weyl, Eddington, and others showed that the apparent recession velocity (the redshift) at small separation would be proportional to the distance, v = ( / 3)^1/2 d.

With Hubble's discovery of the expansion of the Universe in 1929, Einstein's primary justification for introducing the cosmological constant was lost, and he advocated abandoning it. Gamow later wrote that Einstein called this "his greatest blunder," since he could have predicted the expanding Universe. Yet the description above makes it clear that the history was more complicated, and one could argue that in fact Friedmann and Lemaître (or de Sitter) had "predicted" the expanding Universe, or no. Indeed, Hubble noted that his linear relation between redshift and distance was consistent with the prediction of the de Sitter model [Hubble 1929]. Moreover, Eddington recognized that Hubble's value for the expansion rate, H₀ 570 km/s/Mpc, implied a time back to the big bang of less than 2 Gyr, uncomfortably short compared to some age estimates of Earth and the galaxy. By adjusting the cosmological constant to be slightly larger than the Einstein value, = (1 + ) _M/2, a nearly static beginning of arbitrary duration could be obtained, a solution known as the Eddington-Lemaître model. While Eddington remained focused on , trying to find a place for it in his "unified" and "fundamental" theories, was no longer the focus of most cosmologists.

3.2. Steady state and after

Motivated by the aesthetic beauty of an unchanging Universe, [Bondi & Gold 1948] and [Hoyle 1948] put forth the steady-state cosmology, a revival of the de Sitter model with a new twist. In the steady-state model, the dilution of matter due to expansion is counteracted by postulating the continuous creation of matter (about 1 hydrogen atom/m³/Gyr). However, the model's firm prediction of an unevolving Universe made it easily falsifiable, and the redshift distribution of radio galaxies, the absence of quasars nearby, and the discovery of the cosmic microwave background radiation did so in the early 1960s.

was briefly resurrected again in the late 1960s by [Petrosian, Salpeter & Szekeres 1967], who used the Eddington-Lemaître model to explain the preponderance of quasars at redshifts around z ~ 2. As it turns out, this is a real observational effect, but it can be attributed to evolution: quasar activity peaks around this redshift. In 1975, evidence for a cosmological constant from the Hubble diagram of brightest-cluster elliptical galaxies was presented [Gunn & Tinsley 1975], though it was realized [Tinsley & Gunn 1976] that uncertainties in galaxy luminosity evolution make their use as standard candles problematic.

While cosmologists periodically hauled the cosmological constant out of the closet as needed and then stuffed it back in, in the 1960s physicists began to understand that cannot be treated in such cavalier fashion. With the rise of the standard big-bang cosmology came the awareness that the cosmological constant could be a big problem [Zel'dovich 1968]. It was realized that the energy density of the quantum vacuum should result in a cosmological constant of enormous size (see Section 5.1.1). However, because of the success of the hot big-bang model, the lack of compelling ideas to solve the cosmological constant problem, and the dynamical unimportance of at the early epochs when the hot big-bang model was best tested by big-bang nucleosynthesis and the CMB, the problem was largely ignored in cosmological discourse.

3.3. Enter inflation

In the early 1980s the inflationary universe scenario [Guth 1981], with its predictions of a spatially flat Universe ( = 1) and almost-scale-invariant density perturbations, changed the cosmological landscape and helped set the stage for the discovery of cosmic acceleration. When inflation was first introduced, the evidence for dark matter was still accruing, and estimates of the total matter density, then about _M ~ 0.1, were sufficiently uncertain that an Einstein-de Sitter model (i.e., _M = 1) was not ruled out. The evidence for a low value of _M was, however, sufficiently worrisome that the need for a smooth component, such as vacuum energy, to make up the difference for a flat Universe was suggested [Peebles 1984, Turner, Steigman & Krauss 1984]. Later, the model for large-scale structure formation with a cosmological constant and cold dark matter (CDM) and the spectrum of density perturbations predicted by inflation was found to provide a better fit (than _M = 1) to the growing observations of large-scale structure [Turner 1991, Efstathiou, Sutherland & Maddox 1990]. The 1992 COBE discovery of CMB anisotropy provided the normalization of the spectrum of density perturbations and drove a spike into the heart of the _M = 1 CDM model.

Another important thread involved age consistency. While estimates of the Hubble parameter had ranged between 50 and 100 km/s/Mpc since the 1970s, by the mid-1990s they were settling out in the middle of that range. Estimates of old globular cluster ages had similar swings, but had settled at t₀ 13-15 Gyr. The resulting expansion age, H₀ t₀ = (H₀ / 70km/s/Mpc)(t₀ / 14 Gyr) was uncomfortably high compared to that for the Einstein-de Sitter model, for which H₀ t₀ = 2/3. The cosmological constant offered a ready solution, as the age of a flat Universe with rises with ,

(16)

reaching H₀ t₀ 1 for = 0.75.

By 1995 the cosmological constant was back out of the cosmologists' closet in full glory [Krauss & Turner 1995, Ostriker & Steinhardt 1995, Frieman et al. 1995]: it solved the age problem, was consistent with growing evidence that _M was around 0.3, and fit the growing body of observations of large-scale structure. Its only serious competitors were "open inflation," which had a small group of adherents, and hot + cold dark matter, with a low value for the Hubble parameter (~ 50 km/s/Mpc) and neutrinos accounting for 10% to 15% of the dark matter (see, e.g., contributions in [Turok 1997]). During this period, there were two results that conflicted with CDM: analysis of the statistics of lensed quasars [Kochanek 1996] and of the first 7 high-redshift supernovae of the Supernova Cosmology Project [Perlmutter et al. 1997] respectively indicated that < 0.66 and < 0.51 at 95% confidence, for a flat Universe. The discovery of accelerated expansion in 1998 saved inflation by providing evidence for large and was thus welcome news for cosmology.

3.4. Discovery

Two breakthroughs enabled the discovery of cosmic acceleration. The first was the demonstration that type Ia supernovae (SNe Ia) are standardizable candles [Phillips 1993]. The second was the deployment of large mosaic CCD cameras on 4-meter class telescopes, enabling the systematic search of large areas of sky, containing thousands of galaxies, for these rare events. By comparing deep, wide images taken weeks apart, the discovery of SNe at redshifts z ~ 0.5 could be "scheduled" on a statistical basis.

Two teams, the Supernova Cosmology Project and the High-z SN Search, working independently in the mid- to late-1990s took advantage of these breakthroughs to measure the SN Hubble diagram to much larger distances than was previously possible. Both teams found that distant SNe are ~ 0.25 mag dimmer than they would be in a decelerating Universe, indicating that the expansion has been speeding up for the past 5 Gyr [Riess et al. 1998, Perlmutter et al. 1999]; see Fig. 4. When analyzed assuming a Universe with matter and cosmological constant, their results provided evidence for > 0 at greater than 99% confidence (see Fig. 8 for the current constraints).

Figure 4. Discovery data: Hubble diagram of SNe Ia measured by the Supernova Cosmology Project and the High-z Supernova Team. Bottom panel shows residuals in distance modulus relative to an open universe with 0 = M = 0.3. Figure adapted from [Riess 2000, Perlmutter & Schmidt 2003], based on [Riess et al. 1998, Perlmutter et al. 1999].