The Hubble Constant and the Expanding Universe

A reprint from American Scientist the magazine of Sigma Xi, The Scientific Research Society

This reprint is provided for personal and noncommercial use. For any other use, please send a request to Permissions, American Scientist, P.O. Box 13975, Research Triangle Park, NC, 27709, U.S.A., or by electronic mail to [email protected]. ©Sigma Xi, The Scientific Research Society and other rightsholders The Hubble Constant and the Expanding Universe

A newly refined value of H0, the expansion rate of the universe, may herald a first step toward a new era of “precision“ cosmology

Wendy Freedman

may hold the distinction of being the fort. The goal of our work is nothing when the American astronomer Edwin Ionly astronomer to have been trapped less than trying to understand the for- Hubble discovered that our universe is in a cage at the top of a large telescope on mation and evolution of the universe. indeed expanding. He showed that the the 14,000-foot summit of Mauna Kea. (I We do this through observations and farther a galaxy is from us, the faster it know another astronomer who once fell experiments that ultimately provide is speeding away. This velocity- out of such a cage, but that is another sto- numbers as answers—the values of distance relation came to be called ry.) Twenty years ago, before most ob- cosmological parameters. These num- Hubble’s law, and the value that de- servers spent their nights in warm com- bers can tell us something important scribes its current rate of expansion is puter rooms, astronomers commonly about the universe: how much matter H0. Hubble was the first to measure H0 observed in very small cages at the there is, whether the universe is curved (which wasn’t named as such at the prime focus of giant telescopes. Al- or flat, and even how it might all end. time)—deriving a value of 500 kilome- though the long winter nights were al- Understanding the significance of these ters per second per megaparsec. (A most unbearably cold, we had spectacu- numbers and this curious cosmological parsec is equal to 3.26 light-years.) For lar views of the dark night sky, and we quest for parameters requires a brief di- various reasons, Hubble’s result was listened to music through headphones as version into some history. far off the mark, but even a couple of we recorded images and spectra of our The modern science of cosmology is years ago, estimates for H0 varied by a celestial targets. At the end of one night, founded on general relativity—Albert factor of two, generally ranging be- a faulty telescope position caused an ele- Einstein’s theory of gravity—whose tween 50 and 100 (the values are usual- vator to jam, making it impossible for me equations describe the global behavior ly stated without the units of measure). to leave the cage. This was no small in- of matter and energy, and space and This lack of precision was problem- convenience—the closest restroom time. Some solutions to these equa- atic because H0 is a key parameter was 40 feet below, and I was unpleas- tions, notably those devised by the needed to estimate both the age and antly confined within two snowsuits. Russian mathematician Alexander size of the universe. A twofold range in It was another seven hours before a Friedmann in the 1920s, suggest that H0 yields an unacceptably wide span group of engineers arrived from sea the universe originated from a very for the age of the universe—anywhere level (delayed by a flat tire), climbed hot, very dense state in a “big bang“ from 10 to 20 billion years. Such uncer- up the side of the telescope’s dome explosion and that it has been expand- tainty also puts few constraints on cos- and finally pried the elevator free with ing in size ever since. The dynamics of mological models. a crowbar. Now why would an as- the expansion are expressed by the so- But all of this is changing. The value tronomer want to subject herself to called Friedmann equation, which de- of the H0, along with some other cos- such indignities? scribes the evolution of the universe in mological parameters, is becoming in- As an observational cosmologist, I terms of its density and geometry (see creasingly accessible to accurate mea- can say that the rewards more than “Friedmann’s Equation and Cosmological surement as new technologies allow us compensate for the occasional discom- Parameters,” page 42). Applying Fried- to see farther into the universe than mann’s equation requires that we ever before. The Hubble Space Tele- Wendy Freedman is an astronomer at the Carnegie know something about a few parame- scope (HST), which was launched in Observatories in Pasadena, California. Her re- ters it contains—such as H, the Hubble 1990, is among these technological search interests include the evolution of galaxies parameter, which defines the expan- breakthroughs. One of the primary rea- and their stellar populations, and the extragalactic sion rate; Ω , the mass density of the sons the HST was built was to deter- distance scale and cosmology. She was recently m universe; and Ω , the curvature of the mine a more accurate value for H . elected a Fellow of the American Academy of Sci- k 0 ences, and this year was awarded the Magellanic universe. These numbers are not inher- This “Key Project” of the HST program Premium Award of the American Philosophical ently defined by the equation. Instead, was an enormous effort, involving 30 Society. Address: Carnegie Observatories, 813 they remain for us to measure. astronomers (I was one of three co- Santa Barbara Street, Pasadena, CA 91101. Inter- Some of the first efforts to make leaders), spanning eight years of work net: [email protected] these measurements date back to 1929, and about 1,000 hours of HST time. It

© 2004 Sigma Xi, The Scientific Research Society. Reproduction 36 American Scientist, Volume 91 with permission only. Contact [email protected]. Figure 1. Spiral galaxy NGC 4414 is speeding away from us as it is carried by the expansion of the universe. The rate at which the universe is expanding, described by the Hubble constant, is determined simply by measuring the velocities and distances of galaxies. In practice, however, making accurate measurements to distant galaxies can be extremely difficult. The launch of the Hubble Space Telescope in 1990 made such measurements much easier, allowing astronomers to determine the distances to galaxies with an unprecedented level of accuracy. After nearly a decade of measurements, astronomers have derived a value for the Hubble constant that is accurate enough to be used meaningfully in various cosmological and astrophysical calculations. NGC 4414 is nearly 19.1 megaparsecs away (roughly 62 million light-years), and it is receding from us with a speed of about 1,400 kilometers per second. (Image courtesy of NASA, Hubble Heritage Team, STSci/AURA and Wendy Freedman.) was the largest project tackled by HST ing universe and this effect must be ac- number of galaxies distributed across in its first decade, and it was finally counted for or minimized. the sky so that the peculiar motions completed in 2001. A galaxy’s velocity is calculated can be averaged out. from the observed shift of lines in its Measuring distances presents a A Variable and a Constant spectrum (the pattern of electromag- greater challenge. The universe is so In principle, the Hubble constant netic radiation it emits at different large that there is no direct way to should be a straightforward calcula- wavelengths). Galaxies that are mov- measure its full size. There is no cos- tion. It only requires the measurement ing away from us emit light that is mological equivalent to a land survey- of a galaxy’s distance and velocity. In shifted to longer (redder) wavelengths or’s rangefinder—no single method practice, however, devising a method because it is stretched, or “redshifted,” can provide a measure of the uni- to measure distances over cosmologi- by the recession. The greater the shift verse’s absolute size. Instead, as- cal scales is far from trivial. Even rela- in wavelength, the faster the galaxy’s tronomers rely on a series of tech- tively simple velocity measurements velocity. Since the velocity of recession niques, each of which is suitable for a are complicated by the fact that galax- is proportional to its distance (Hub- certain range of distances, and together ies tend to have other galaxies as ble’s law again), the farther the dis- these methods constitute the “cosmo- neighbors, and so they interact gravita- tance measurements can be made, the logical distance ladder.” tionally, perturbing one another’s mo- smaller the proportional impact of pe- For the nearest stars, distances can tions. These peculiar velocities are dis- culiar velocities on the overall expan- be measured by trigonometric parallax, tinct from the recession velocities (the sion velocity. Astronomers can further which uses the baseline of the Earth’s Hubble flow) of galaxies in the expand- reduce the uncertainty by observing a orbit for triangulating a star’s distance

a Cepheid’s periodicity Cepheid period-luminosity relation

time (days) 131030 100 period (days)

Cepheids are massive stars (at least three times greater than the Sun) that have reached an unstable point in their evolution. During the Cepheid phase, the outer atmospheres of these stars pulsate—changing in size and color (left)—and therefore in their brightness, or luminosity, over a very regular period, ranging from 2 to more than 100 days. (A Cepheid’s brightness is determined more by its color than its size.) Brighter stars have longer periods, in a linear relation (right), allowing scientists to gauge a star’s luminosity on the basis of its period. The inverse-square law of radiation then allows astronomers to determine the absolute distance to the Cepheid. The Cepheid distance scale itself is calibrated indirectly by measurements of these stars in a satellite galaxy of the Milky Way, the Large Magellanic Cloud, whose distance is determined by a combination of methods.

using simple, high-school trigonome- intrinsically bright stars, so they can be galaxies. For example, the Tully-Fisher re- try. Distant stars in our galaxy and ex- observed in galaxies outside the Milky lation states that the rotational velocity of tragalactic objects require other, less di- Way. In fact, Hubble discovered other a spiral galaxy is correlated to its lumi- rect indicators of distance. In these galaxies outside of the Milky Way by nosity: Intrinsically bright galaxies rotate instances, astronomers rely on objects measuring Cepheid variables. These and faster than dim ones. This relation has that exhibit a constant brightness—so- other distances enabled him to deter- been measured for hundreds of galaxies, called “standard candles”—or those mine that the universe is expanding. and there appears to be an excellent cor- whose brightness is related to some The key to observing Cepheids in relation. There is an analogous relation quality of the object that is indepen- other galaxies is a telescope with suffi- for elliptical galaxies, in which the stars dent of distance, such as its period of cient resolving power to distinguish in the brightest galaxies tend to have a oscillation or its rotation rate or its col- these stars from others that contribute greater range of orbital velocities (a high or. The standard candles must then be to the overall light of the galaxy. This is velocity dispersion). A third method independently calibrated to an ab- where the HST came to play a central takes advantage of the fact that the abili- solute unit of measure so that the true role. Because it orbits above our plan- ty to resolve the stars in a galaxy de- distance can be determined. et’s turbulent atmosphere, the space creases as its distance increases. For ex- The most precise method for measur- telescope’s resolution is about ten times ample, an image of a nearby galaxy ing distances is based on the observation better than that obtained by telescopes might have an average of 10 stars per of Cepheid variables—stars whose at- on Earth. Thus the HST opened up the pixel (or individual picture element), mospheres pulsate in a very regular way possibility of observing Cepheids in a whereas a distant galaxy would have a for periods from 2 to more than 100 days. volume of extragalactic space a thou- larger number, perhaps 1,000 stars for In the early part of the 20th century, the sandfold greater than previously possi- every pixel. The near galaxy would ap- American astronomer Henrietta Leavitt ble. (Recall that volume increases with pear grainy with relatively large fluctua- discovered a relation between the aver- the cube of the linear distance.) With the tions in its overall surface brightness, age intrinsic brightness (or luminosity) HST, Cepheids can be measured out to whereas the distant galaxy would ap- of a Cepheid and its pulsation period: the nearest massive clusters of galaxies pear smoother. Each of these methods Brighter stars had longer periods (see about 30 megaparsecs away (Figure 2). can be usefully applied for galaxies up above). Knowing its intrinsic brightness, Beyond this distance, other methods are to 150 megaparsecs away. astronomers can deduce a Cepheid’s dis- needed to extend the extragalactic dis- Among the most promising cosmo- tance because the star’s apparent bright- tance scale (Figure 4). logical distance indicators is the peak ness decreases with the inverse square of Three of these methods rely on the brightness of type Ia supernovae (Fig- its distance. Cepheids also happen to be global properties of spiral and elliptical ure 3). These explosions occur in a bi-

© 2004 Sigma Xi, The Scientific Research Society. Reproduction 38 American Scientist, Volume 91 with permission only. Contact [email protected]. nary star system when material from a 2,000 companion star falls onto a white =75 0=83 H 0 dwarf star. The extra mass exceeds the H =67 white dwarf’s level of stability (the H 0 Chandrasekhar limit), causing it to col- 1,500 lapse. This detonates the explosive burning of carbon, and the entire star blows up, briefly shining as brightly as a whole galaxy. The shape of the su- 1,000 pernova’s light curve (a plot of how its brightness changes with time) is in- dicative of its peak luminosity: Bright 500 supernovae tend to have shallower Cepheids in curves (just as bright Cepheids have velocity (kilometers per second) individual galaxies longer periods), and the relative luminosity of the supernova can be deter- 0 mined quite accurately. Because super- 0102030 novae are so bright, they can be used to distance (megaparsecs) measure H0 out to where recession velocities approach 30,000 kilometers per Figure 2. Measures of the velocities and distances of galaxies in this Hubble diagram, based second (about 400 megaparsecs), and solely on Cepheid variable stars in 22 galaxies, yield a Hubble constant (H0) value of 75 kilo- the effects of a galaxy’s peculiar mo- meters per second per megaparsec (slope of the solid line). Because Cepheids can only be ac- tion drop to less than one percent. (Pe- curately measured to a distance of 20 or 30 megaparsecs, several other methods were combined culiar velocities of galaxies typically to determine a more accurate value for H0 (see Figure 4). (Error values of plus or minus about 10 amount to about 200 to 300 kilometers percent are shown by the dashed lines.) per second.) Another kind of stellar explosion, a type II supernova, can also serve as a distance indicator. Type II supernovae are produced by massive stars of various sizes and show a wider range of luminosity than type Ia supernovae. Al- though they are not standard candles, type II supernovae can reveal their distance through spectroscopic measurements of their expanding atmospheres and photometric measures of their an- gular size. These supernovae currently provide distances to 200 megaparsecs. These distance indicators provide a means of measuring the relative distances to the galaxies. As with any map, however, we need an absolute scale. The calibration for all these methods is currently based on the Cepheid distance scale—the bottom rung on the distance ladder—and so these methods are con- sidered to be secondary. (In principle, the type II supernovae can provide absolute measures of distance, but they were calibrated to the Cepheids for our work.) With one exception, all of the secondary distance indicators are calibrated directly by measuring Cepheid distances in galaxies that display one or more of the properties employed by the secondary method. The velocity-dispersion tech- nique for elliptical galaxies cannot be cal- Figure 3. Type Ia supernovae, such as supernova 1994D (bright spot, lower left) in the spiral galaxy NGC 4526, can be used as a distance marker by determining its relative brightness. ibrated directly by Cepheids. Instead, Such supernovae have played a dual role in cosmology. Type Ia supernovae within 400 mega- this method was indirectly calibrated by parsecs are used to estimate H0, but beyond this distance the Hubble-diagram plot of their ve- the Cepheid distances to clusters of locities and distances is no longer linear. This break from linearity in the distant universe re- galaxies containing these elliptical galax- veals that the expansion rate of the universe is actually accelerating—a phenomenon that few ies, and it has the largest uncertainties. scientists expected. (Image courtesy of High-Z Supernova Search Team, HST and NASA.)

low high velocity velocity dispersion dispersion

intrinsically intrinsically intrinsically intrinsically dimmer brighter dimmer brighter

shallow steep decay decay brightness umber of stars brightness umber of stars n n time time stellar velocity stellar velocity

useful distance 400 megaparsecs useful distance 150 megaparsecs

Tully-Fisher relation surface brightness for elliptical galaxies

grainy smooth appearance appearance

slow rapid rotation rotation

intrinsically intrinsically dimmer brighter near far

useful distance 150 megaparsecs useful distance 150 megaparsecs

Figure 4. Secondary distance indicators are used to measure the Hubble constant far out in the universe (up to 400 megaparsecs or 1.3 billion light- years away). Each of these four methods provides an independent way of measuring the relative distance to a galaxy. In each instance, some mea- surable property is correlated with the intrinsic brightness or relative distance of the object. Thus, the light curves of intrinsically brighter type Ia supernovae have a shallow decay (upper left), the stars in intrinsically brighter elliptical galaxies have a wider range of velocities (upper right), intrinsically brighter spiral galaxies rotate more quickly (lower left), and distant elliptical galaxies have a smoother appearance than near ones (lower right). The relative distances determined with these methods are calibrated (directly or indirectly) to the Cepheid distance scale. ≈ H0 72 yond 5,000 kilometers per second the past, so the estimated age of the Although each of the secondary dis- (about 70 megaparsecs away), where universe would be younger than if it tance methods provides a estimate of the effects of peculiar motions are had always been expanding at the H0 on its own, the HST Key Project small compared to the Hubble flow. same rate. (Because a faster rate would was designed to avoid the pitfalls of re- So what does 72 mean? Recall that allow the universe to reach the “same lying on a single method, so our study H0 is the current expansion rate of the place” in less time.) And this decelera- combined the results of the various ap- universe. Although the Hubble con- tion is what astronomers expected to proaches. Even so, readers should note stant is the most important parameter find as they looked farther out into the that there is a reasonable level of agree- in constraining the age of the universe, universe, and further back in time. ment for the value of H0 among the dif- determining a precise age requires that We get an inkling that something ferent methods: Cepheids, 75; type Ia we know how the current expansion isn’t right with this picture if we calcu- supernovae, 71; Tully-Fisher relation, rate differs from its rate in the past. If late the age of the universe assuming 71; velocity dispersion in elliptical the expansion has slowed or accelerat- that it is slowing down. With a Hubble galaxies, 82; surface brightness fluctua- ed, then calculations of its age must constant of 72, a decelerating universe tions, 70; and type II supernovae, 72. A take this into consideration. turns out to be only 9 billion years old. weighted average of these values Until recently, cosmologists general- The problem is that we know of stars yields an H0 of 72 ± 8. This conver- ly believed that the gravitational force in our galaxy that are at least 12 billion gence can be seen graphically (Figures 5 of all the stuff in the universe has been years old. Since the stars cannot be old- and 6) and is especially notable for slowing its expansion. In this view the er than the universe, something must galaxies with redshifted velocities be- expansion would have been faster in be wrong. The good agreement among

© 2004 Sigma Xi, The Scientific Research Society. Reproduction 40 American Scientist, Volume 91 with permission only. Contact [email protected]. several independent ways of estimat- 30,000 2 =7 ing the ages of ancient stars gives as- 0 =79 H tronomers confidence that these stellar H 0 ages are not in error. =65 The resolution of the problem turns H 0 out to be a newly discovered property of the universe itself. In 1998, two 20,000 groups of astronomers studying distant supernovae reported something remarkable: Type Ia supernovae that are far out in the universe appear to be dimmer than expected. Although it’s possible (though there is no evidence) 10,000 that supernovae were intrinsically Tully-Fisher velocity dispersions dimmer in the distant past, the sim- velocity (kilometers per second) plest explanation is that these explo- surface brightness sions are actually farther away than supernovae Ia they would be if the universe were re- supernovae II ally slowing down. Instead of deceler- 0 ating, the type Ia supernovae suggest that the expansion of the universe is ac- 0 100 200 300 400 celerating (Figure 7). This acceleration distance (megaparsecs) has now been supported by further studies, and many astronomers now Figure 5. Hubble diagram of five secondary-distance indicators reveals a combined average believe that there must be a previously H0 value of 72, the final result of the Hubble Key Project. Integrating this H0 value into the unrecognized repulsive force in the Friedmann equation (see page 42) suggests that the universe has been expanding for about 13 universe—something that acts against billion years. gravity. It is being called dark energy. Ω To a certain extent the existence of So how do we estimate the expan- term, k. Inflationary theory (a very dark energy may have been anticipated sion age of the universe in light of these successful cosmological model that by Einstein. Even before the expansion results? Using the Friedmann equation, posits an extremely rapid expansion of the universe was discovered, Ein- an accurate estimate requires not only very early in the universe) and obser- stein’s original equations that described the value of H0, but also the density pa- vations of the cosmic background radi- Ω Ω the evolution of the universe contained a rameters, m and Λ, and the curvature ation currently support a so-called term that he called the cosmological constant (Λ, lambda). Because the astronomers of his day assured him that the universe was not in motion, Einstein introduced the term to prevent any ex- 100 pansion or contraction, which would result naturally from the effects of gravity. per second (The cosmological constant, Λ, appears 5,000 kilometers in the Friedmann equation.) When Hub- 80 ble discovered the expansion, Einstein H =72 apparently referred to the cosmological 0 constant as his greatest blunder: It didn’t seem necessary, and he had missed the 60 opportunity to predict the expansion. Tully-Fisher Until a few years ago, cosmologists velocity dispersions generally set the Λ term to zero in surface brightness

Friedmann’s equation. However, the (kilometers per second megaparsec) 40 supernovae Ia 0 discovery that the universe is acceler- H supernovae II ating suggests that the term may have been necessary after all. The cosmo- 0 logical constant may represent dark 0 100 200 300 400 energy, or the vacuum energy density distance (megaparsecs) (ΩΛ). ΩΛ has some very curious properties. It can bend space in much the Figure 6. Value of the Hubble constant converges toward 72 as the recession velocities of same way that matter does, and so galaxies are measured to ever greater distances by the secondary distance indicators. Beyond a contribute to the overall geometry of recession velocity of about 5,000 kilometers per second (about 70 megaparsecs away), the ef- the universe, but it exerts a “negative fects of a galaxy’s peculiar motions (caused by gravitational interactions with other galaxies) is pressure” that causes the accelerated reduced to less than 5 percent of its overall velocity. These distant galaxies provide a more ac- expansion we observe. curate measure of H0. © 2004 Sigma Xi, The Scientific Research Society. Reproduction with permission only. Contact [email protected]. 2003 January–February 41 Friedmann’s Equation and Cosmological Parameters

To simplify his calculations, Albert Einstein adopted two convenient mathematical approximations: He assumed the universe was both homogeneous (having the same density everywhere) and isotropic (the same in every direction). Remarkably, modern observations suggest that these assumptions are also very good approximations to the real universe. The general theory of relativity suggests that the evolution of such a universe can be described by the Friedmann equation:

0 0.1 0.2 0.3 80 0.4 0.5 60 100 0.6 0.7 0.8 40 120 0.9 1.0 20 140 =– +ΩΛ kilometers 0 per second 160 per megaparsec Ωm

8πGρm k H 2 =–+ 3 r 2 3 Hubble mass curvature of vacuum energy parameter density the universe density

ρ where H is the Hubble parameter, G is Newton’s gravitational constant, m is the average mass density of the universe, k is the curvature of the universe, r is the scale factor (the relative distance of galaxies as a function of time), and Λ is the cosmological constant (introduced by Einstein). This equation allows us to determine both the age and size of the universe if we can measure some of the parameters. 2 Ω π ρ 2 Ω 2 2 If we divide both sides of the equation by H , we get the mass density, m = 8 G m/3H ; the curvature term, k = – k/r H ; Ω Λ 2 Ω Ω Ω and the vacuum energy density, Λ = /3H . This provides the relation m + k + Λ = 1. Ω Measurements of the cosmic microwave background indicate that the universe is flat, k = 0, so the curvature term drops out, Ω Ω and the evolution of the universe is described merely by m and Λ. Recent observations suggest that the universe is dominated not by matter, but rather by the vacuum energy, which exerts a negative pressure that accelerates its expansion.

Ω “flat” universe, where k = 0, so the as planet-like bodies or warm inter- What’s Next? curvature term drops out. In a flat uni- galactic gas. This normal matter A few decades ago, the universe Ω Ω verse m + Λ = 1 (by definition). (made of baryons, such as protons seemed a much simpler place. It ap- The mass density of the universe, and neutrons) adds up to no more peared to be composed of ordinary Ω m, must be determined by observa- than 5 percent of the critical density. matter, and the expansion of the uni- tion and experiment. Figuring this one Another 25 percent (and the rest of the verse could be described by the Hub- out is tricky. The rotational velocities dark matter) appears to be in the form ble constant and the matter density of galaxies and the dynamics of galac- of exotic (non-baryonic) matter, which alone. Today there is powerful evi- tic clusters suggest that the visible is believed to consist of as yet un- dence that non-baryonic matter makes matter in the universe, the stuff that known particles that interact with up about one third of the total mass- makes up stars and bright nebulae, baryonic matter almost exclusively plus-energy density. And new data constitutes only a fraction of its total through gravity. That brings the total suggest that the universe is accelerat- mass. The rest appears to be some mass density of the universe to 30 per- ing, pointing to the existence of a mys- Ω form of invisible material, or dark mat- cent (or m = 0.3). So, in a flat uni- terious dark energy that makes up ter, which interacts gravitationally verse, the vacuum energy density most of the other two thirds. As yet, with these luminous bodies and so al- must be about 70 percent (ΩΛ = 0.7) of theory can provide no explanation for ters the dynamics of galaxies and clus- the total mass-plus-energy density. the dark energy. In fact, calculations ters of galaxies. Stars and bright nebu- Now, by integrating the Friedmann based on modern particle physics dis- lae appear to account for merely 1 equation with these density values, agree wildly with the observations percent of the matter and energy in and an H0 value of 72, we derive an (and this was the case even when the the universe. Another 4 percent might age for the universe of about 13 ± 1 cosmological constant was thought to be accounted for by nonluminous billion years, a value that agrees nicely be zero). Hence, astronomical observa- bodies (some of the dark matter), such with the ages of the oldest stars. tions are hinting at fundamentally new

future

present

past Ω m > 1 Ω m < 1

Ω Ω m < 1, Λ > 0

Ω Figure 7. Evolutionary course of the expanding universe depends on the total amount of matter it contains. The parameter m is the ratio of the actu- al density of the matter in the universe relative to the critical value, which marks the dividing line between a universe that expands forever and one Ω that ultimately collapses again. The critical value is defined as m = 1, where there is just enough matter in the universe to prevent its eternal expan- Ω sion or eventual collapse. In a “closed” universe, with m > 1, the gravitational pull of matter ultimately causes the universe to collapse in a “big Ω crunch.” In an “open” universe, with m < 1, there is not enough matter to gravitationally halt the expansion, and so it continues forever. As- Ω Ω tronomers have determined that we live in a universe with m < 1, but that a dark (or vacuum) energy ( Λ > 0) appears to be causing the expansion to accelerate. Each of these models also implies a different age for the universe, based on its current expansion rate. (Adapted from a NASA illustration.) physics, and a universe in which 95 are making careful measurements of Michigan Center for Theoretical Physics, ed. M. J. percent of the total mass and energy is the universe’s acceleration, and plans Duff and J. T. Liu. Singapore: World Scientific. in new exotic forms. are under way to build a satellite large- Preprint: http://arXiv.org/abs/astro- ph/0202006 It is an exciting time in cosmology. ly dedicated to this effort. Encoded Goldsmith, D. 2000. The Runaway Universe. Gone are the days, perhaps, of the lone within the small fluctuations of the cos- Cambridge, Mass.: Perseus Publishing. astronomer sitting in a prime-focus cage. mic microwave background radiation Guth, A. H. 1997. The Inflationary Universe. But a suite of planned observations and is information about all of these cos- Reading, Mass.: Perseus Books. experiments are ushering in a new era mological parameters. An explosion of with unprecedented precision. Signifi- technical capabilities is yielding com- cant improvements to the measurement pletely independent measures of these of the Hubble constant will come by the parameters and checks on the other end of the decade with the launch of methods. We may not yet have a com- new satellite interferometers—SIM, the plete view, but there is no question that Space Interferometry Mission, planned we are in the midst of a revolution in by NASA, and GAIA, a European Space our thinking about the nature of the Links to Internet resources for further Agency project. These instruments will universe we live in. be capable of delivering 100 to 1,000 exploration of “The Hubble Constant and times more accurate trigonometric par- Bibliography the Expanding Universe” are available on allax distances to Cepheids within our Ferguson, K. 1999. Measuring the Universe. New the American Scientist Web site: galaxy—measurements that are used to York: Walker and Company. calibrate the extragalactic Cepheids. The Freedman, W. L., et al. 2001. Final results from http://www.americanscientist.org/ the Hubble Space Telescope Key Project to Cepheid calibration is currently the measure the Hubble constant. The Astro- issueTOC/issue/347 largest remaining uncertainty in the HST physical Journal 553:47–72. Key Project measurement of H . Freedman, W. L. 2002. The expansion rate of the 0 universe. Astronomy and Geophysics 43:10–13. Many experiments are searching for Freedman, W. L. In press. The measure of cos- the weakly interacting particles that mological parameters. In A Spacetime Odyssey: could be the dark matter. Large teams Proceedings of the Inaugural Conference of the