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Proc. Natl. Acad. Sci. USA Vol. 94, pp. 6579–6584, June 1997 From the Academy

This paper summarizes a symposium that was one of the Frontiers of Science symposia held November 2–4, 1995, at the Arnold and Mabel Beckman Center of the National Academy of Sciences and Engineering in Irvine, CA.

The age of the *

DAVID N. SPERGEL†‡,MICHAEL BOLTE§, AND WENDY FREEDMAN¶

†Department of Astronomy, University of Maryland, College Park, MD 20742; ‡Department of Astrophysical Sciences, Princeton University, Princeton, NJ 08544; §Lick Observatory, University of California, Santa Cruz, CA 95064; and ¶Carnegie Observatories, Pasadena, CA 91101-1292

The theory is a remarkably simple theory built on two massive than the , is blue and very luminous, whereas pillars: the theory of and the assumption that , which is less massive than the Sun, is red and the universe is isotropic and homogeneous on large scales. This less luminous. theory has had a number of important successes: it can explain The fundamental fuel for a ’s luminosity is mass. In any the observed expansion of the universe; the thermal micro- of the fusion reactions that result in hydrogen conversion to wave background radiation; the observed abundances of deu- helium, a small amount of mass is transformed into energy terium, helium, and lithium; and the rapid evolution seen in in the form of and ␥-rays: the neutrinos flee the distant (see refs. 1 and 2 for recent reviews). Yet this scene and the ␥-rays are immediately absorbed, providing successful model faces a potential crisis: the age of the oldest the heat source for the star. Because have only a limited stars may exceed the predicted age of the universe. In the first supply of hydrogen in their cores, they have a limited half of the session, Michael Bolte of the University of Cali- lifetime, ␶MS, on the . This lifetime is propor- fornia, Santa Cruz, described efforts to measure the age of the tional to iM͗͞L͘, where i is the fraction of the total mass of oldest stars. Because the oldest stars ought to be younger than the star, M, available for nuclear burning in the core, and ͗L͘ the universe, this places a lower bound on t0, the age of the is the time average luminosity of the star on the main universe. In the second half of the session, Wendy Freedman sequence. Because of the strong dependence of luminosity Ϫ2.5 of the Carnegie Observatories discussed measurements of the on stellar mass, ␶MS ϰ M , it is fortunate that our Sun is not more massive because high-mass stars rapidly exhaust Hubble constant, H0, the rate of expansion of the universe. In the simplest and best explained version of the big bang their core hydrogen supply. Once a star exhausts its core theory—a flat, matter-dominated universe—the age of the hydrogen supply, the star becomes redder, larger, and more luminous, and it moves off the main sequence and becomes universe is 2͞3H0. The final section of this paper is based on the panel discussion of the implications of their results. The a red giant star. Appendix describes the relationship between the age of the Astronomers find it convenient to represent the properties universe and the Hubble constant in different and of stars on a Hertzsprung–Russell (HR) diagram, a plot of a explains why many cosmologists believe that the universe is star’s luminosity and surface temperature. For historical rea- flat. sons, optical astronomers like to plot the magnitude of a star, Ϫ2.5 times the base 10 logarithm of its luminosity, on the y axis, Determining the Ages of the Oldest Objects and the temperature of the star on the x axis. To further obscure the field, temperature increases to the left on the Because the first generation of stars formed some time after diagram. the big bang, the age of the oldest known stars places a lower The HR diagram is a particularly useful way to display the limit on the age of the universe. properties of stars in a cluster. A cluster is a dense collection of stars that are thought to have all formed at about the same Theory of . Stars are remarkably simple time (give or take a million ). A very young cluster has systems: they are slowly evolving, nearly spherical clouds main-sequence stars over a broad range of masses (and composed mostly of hydrogen and helium that can be accu- luminosities and temperatures). A 2 billion--old cluster rately modeled on a computer. The basic physics needed to contains main-sequence stars up to a ‘‘turn-off mass’’ of 2 solar model the structure and evolution of stars is mostly well masses—more massive stars exhaust their core hydrogen sup- understood: nuclear cross-sections, the equation of state of ply in under 2 . A 10 billion-year-old cluster matter, and the physics of hydrostatic equilibrium and radia- contains main-sequence stars up to a ‘‘turn-off mass’’ of 1 solar tion transfer. Although stellar structure does depend some- mass. A 15 billion-year-old cluster would contain no main- what on the physics of convection, which remains poorly sequence star more massive than 0.85 solar mass and no understood, stellar ages are relatively insensitive to the details main-sequence star more luminous than Ϸ0.5 times the lumi- of convection. nosity of the Sun. Thus, by determining the maximum lumi- Main-sequence stars are stars, like our Sun, that fuse nosity of a main-sequence star in a cluster, astronomers can hydrogen to helium in their cores. For a given chemical measure its age. composition and stellar age, a star’s luminosity, the total Astronomers, however, cannot measure the luminosity of a energy radiated by the star per unit time, depends only on its star directly; they can only measure the flux from a star, F.If mass. Stars that are 10 times more massive than the Sun are the distance to the cluster, D, can be determined, then energy more than 1,000 times more luminous than the Sun. We should not be too embarrassed by the Sun’s low luminosity: it is 10 Abbreviations: HR, Hertzsprung–Russell; HST, Hubble Space Tele- times brighter than a star of half its mass. More massive scope. main-sequence stars are also bluer (higher surface tempera- *This paper is part of the fourth installment of the new feature, “From tures) than less massive stars. Thus, Sirius, which is more the Academy.” The first installment appeared in the March 4, 1997 issue, the second in the April 1, 1997 issue. “From the Academy” will be presented occasionally as new NRC reports appear and as essays © 1997 by The National Academy of Sciences 0027-8424͞97͞946579-6$2.00͞0 on the NAS are prepared.

6579 Downloaded by guest on September 26, 2021 6580 From the Academy: Spergel et al. Proc. Natl. Acad. Sci. USA 94 (1997)

conservation implies that L ϭ 4␲D2F. The challenge, and the Nature offers astronomers a wonderful laboratory for test- major source of uncertainty in age determination, is measuring ing stellar models with double-line, eclipsing binary stars. the distance to stellar clusters. Astronomers can measure the period of these binaries, their Age determinations also depend on the star’s chemical velocities, and the inclination of their orbits. With these composition: a star’s evolution depends on its initial abun- measurements, it is possible to determine their masses to dance of helium, carbon, oxygen, and iron, because these better than 1%. In probably their most stringent test, the elements (and other less common elements) all affect the rate observed mass, luminosities, and temperature are in excellent at which can escape from the core of a star and, agreement with the stellar models. Future surveys should be particularly in the case of oxygen, moderate the energy gen- able to detect more of these systems. Their detection and study eration reactions. Because the oldest stars have very low in a (see below) would be an important abundances of these elements, stellar age estimates for the confirmation of the inferred ages. globular clusters are, fortunately, not very sensitive to these Observing Old Stars in Old Clusters. Globular clusters are details. thought to be the oldest clusters in the . Globular Should We Believe the Models? Stellar models are needed clusters are dense spherical clusters of stars that are on orbits to relate the observed luminosity and surface temperature of that suggest that they were formed in the initial collapse of our a star to its core mass and its time average luminosity, so that Galaxy. Their stellar densities are so high that the Hubble we can determine its main-sequence lifetime. Fortunately, the Space Telescope (HST) was needed to resolve their dense current stellar models are thought to be very reliable in the cores (see Fig. 1). Globular clusters are iron-poor: the relative relevant mass range. The models are less reliable for very abundance of iron to hydrogen in a globular cluster star is only low-mass stars that contain complex molecules in their outer 1͞10 to 1͞150 of the relative abundance in the Sun. These stars atmospheres and for higher-mass stars, whose cores are altered are also depleted in carbon, oxygen, and all of the other by convection. elements heavier than lithium. Because all of the elements The stellar models correctly predict the age and structure of heavier than lithium are synthesized in stars, these low abun- the Sun. The age, total luminosity, surface temperature, and dances suggest that globular clusters formed very early in the chemical composition of the Sun are accurately known and are history of the Galaxy before multiple generations of stars built well matched by the models (although, as the Sun is an up element abundances. important calibration point, this by itself is slightly suspect as Fig. 2 shows an HR diagram for M92, an extremely iron-poor a test of the models). The Sun also sustains an astonishingly globular cluster. The most iron-poor clusters also appear to be large number of vibrational modes, and by studying the Sun’s the oldest. The distance to the cluster was estimated by oscillations, astronomers have measured the properties of the requiring that the main-sequence stars in the cluster have the interior of the Sun, just as geologists have probed the ’s same luminosity as nearby subdwarf stars with the same interior with seismology. The solar models agree remarkably temperature (4). The lines on the plot are the model curves for well with the Sun’s observed properties (3). 12, 14, 16, and 18 billion-year-old clusters with the appropriate The stellar models also correctly predict the temperature– chemical abundances. Fitting the data and propagating all of luminosity relation for the nearby subdwarfs, main-sequence the observational errors implies a cluster age of 16 Ϯ 2 billion stars with chemical properties similar to stars in the oldest years, a minimum age for the universe. clusters. These stars are so close to the that their distance can be determined by trigonometric parallax, so their Measuring the Expansion Age of the Universe luminosity can be accurately measured. There are now 11 dwarfs with accurate parallax distance: their luminosities and Historical Overview. In the 1920s, , using the temperatures agree with model predictions (4). newly constructed 100-inch telescope at Mount Wilson Ob-

FIG. 1. Public archive HST image of M15, one of the nearby globular clusters. (Image taken by P. Guhathakurta. This figure was created with support to the Space Telescope Science Institute, operated by the Association of Universities for Research in Astronomy, Inc., from NASA contract NAS5-26555, and is reproduced with permission from AURA͞STScI.) Downloaded by guest on September 26, 2021 From the Academy: Spergel et al. Proc. Natl. Acad. Sci. USA 94 (1997) 6581

Hubble’s second revolutionary discovery was based on his plot (shown as Fig. 3) of galaxy distance determinations and measurements of the relative velocities of these galaxies. He showed that more distant galaxies were moving away from us more rapidly: the universe was not static, but rather was expanding. This discovery marked the beginning of the mod- ern age of . Today, Cepheid variables remain the best method for measuring distances to galaxies and are vital to determining the expansion rate and age of the universe. What Are Cepheid Variables? The structure of all stars, including the Sun and Cepheid variable stars, is determined by the opacity of matter in the star. If the matter is very opaque, then it takes a long time for photons to diffuse out from the hot core of the star, and strong temperature and pressure gradients can develop in the star. If the matter is nearly transparent, then photons move easily through the star and erase any temperature gradient. Cepheid stars oscillate be- tween two states; when the star is in its compact state, the helium in a layer of its atmosphere is singly ionized. Photons scatter off of the bound in the singly ionized helium atoms. Thus, the layer is opaque, and large temperature and pressure gradients build up across the layer. These large pressures cause the layer (and the whole atmosphere) to expand. When the star is in its expanded state, the helium in FIG. 2. HR diagram for M92. The squares are measured colors and the layer is doubly ionized, so that the layer is more transparent brightnesses for individual stars in the cluster. The lines show model to radiation and there is a much weaker pressure gradient predictions for the positions of stars for cluster ages of 14, 16, and 18 across the layer. Without the pressure gradient to support the billion years. The match of the models to the cluster data for an age star against gravity, the layer (and the whole atmosphere) of 16 billion years is remarkably good. contracts, and the star returns to its compressed state. Cepheid variable stars have masses between 5 and 20 solar servatory, detected variable stars in several nebulae, diffuse masses. The more massive stars are more luminous and have objects whose nature was a topic of heated debate in the more extended envelopes. Because their envelopes are more astronomical community. His discovery was revolutionary, for extended and the density in their envelopes is lower, their these variable stars had a characteristic pattern resembling a variability period, which is proportional to the inverse square class of stars called Cepheid variables. Earlier, Henrietta root of the density in the layer, is longer. Leavitt, part of a group of female astronomers working at Difficulties in Using Cepheids. A number of difficulties have Harvard College Observatory, had shown a tight correlation been associated with using Cepheids as distance indicators. between the period of a Cepheid variable star and its intrinsic Until recently, astronomers used photographic plates to mea- luminosity. Thus, Hubble, by measuring the period of these sure the fluxes from stars. The plates had a highly nonlinear stars and their fluxes, showed that these nebulae were not response and often produced inaccurate flux measurements. Because massive stars are short lived, they are always located clouds within the but were external galaxies far near their dusty birthplaces. Dust absorbs light, particularly at beyond the edge of our own Galaxy. blue wavelengths where most photographic images were taken, and if not properly corrected for, this dust absorption could lead to erroneous luminosity determinations. Finally, it has been difficult to detect Cepheids in distant galaxies from the ground because Earth’s fluctuating atmosphere makes it im- possible to separate these stars from the diffuse light of their host galaxies. Another historical difficulty with using Cepheids as distance indicators has been the problem of determining the distance to a sample of nearby Cepheids. In recent years, astronomers have developed several reliable and independent methods of determining the distances to the Large Magellanic Cloud (LMC), one of the satellite galaxies of our own Milky Way Galaxy. Because the LMC contains large numbers of Cep- heids, it can be used to calibrate the distance scale. Recent Progress. Recent technological advances have en- abled astronomers to overcome a number of the other past difficulties. New detectors called CCDs (charge-coupled de- FIG. 3. This figure shows Hubble’s original diagram (5). Plotted on vices) make accurate flux measurements possible. These new the y axis is v, the velocity of each galaxy in his sample relative to the detectors are also sensitive in the infrared wavelengths. Dust Milky Way in km͞s. Plotted on the x axis is the Hubble’s inferred is much more transparent at these wavelengths. By measuring distance to the galaxy, d, in parsecs (pc). Because of calibration fluxes at multiple wavelengths, astronomers are able to correct problems, Hubble’s original distance estimates were off by nearly an for the effects of dust and make more accurate distance order of magnitude. One parsec is approximately 3 light years or 3 ϫ 1016 meters. ‘‘Hubble’s law’’ is a linear relationship between velocity determinations. These advances enabled accurate study of the nearby gal- and distance: v ϭ H0d, where H0, the slope of the line in the diagram, has units of km͞s͞Mpc (where 1 Mpc ϭ one million parsecs). Hubble’s axies that comprise the ‘‘Local Group.’’ Astronomers observed constant, H0, can be rewritten in more conventional units: 100 Cepheids in both the metal-rich inner region of M31 (An- km͞s͞Mpc Ϸ 1 ϫ 10Ϫ10 yrϪ1. dromeda) and its metal-poor outer region (6). This work Downloaded by guest on September 26, 2021 6582 From the Academy: Spergel et al. Proc. Natl. Acad. Sci. USA 94 (1997)

showed that the properties of Cepheids did not depend factor 2 uncertainty, is one of the most important outstanding sensitively on chemical abundances. Despite these advances, problems in . astronomers, limited by the Earth’s atmosphere, could only Hubble Key Projects. One of the key projects of the HST measure the distances to the nearest galaxies. In addition to the is to complete Edwin Hubble’s program of measuring dis- motion due to the expansion of the universe, galaxies have tances to nearby galaxies. Although the HST is comparable ‘‘relative motions’’ due to the gravitational pull of their in diameter to the Carnegie Institution’s telescope on Mount neighbors. Because of these peculiar motions, astronomers Wilson used by Hubble, it has the advantage of being above need to measure the distances to distant galaxies so that they the Earth’s atmosphere, rather then being located on the can determine the Hubble constant. outskirts of Los Angeles. Thus, HST can resolve Cepheids in To push deeper into the universe, astronomers have devel- more distant galaxies. The key projects aim to determine the oped a number of new techniques for determining relative distances to 20 nearby galaxies. With this large sample, HST distances to galaxies. These independent relative distance can calibrate and cross-check a number of the secondary distance indicators. HST will also be able to check if the scales now agree to better than 10% (7). For example, there is properties of Cepheid variables are sensitive to stellar com- a very tight relation, called the Tully–Fisher relation, between position. the rotational velocity of a spiral galaxy and its luminosity (8). NASA’s repair of the HST restored its vision and enabled Astronomers also found that type Ia supernovae, which are the key project program. Fig. 4 shows several images of M100, thought to result from the explosive burning of a dwarf, one of the nearby galaxies observed by the key project pro- all had nearly the same peak luminosity (9). However, without gram. Note that with the refurbished HST, it is much easier to accurate measurements of distance to large numbers of pro- detect individual bright stars in M100, a necessary step in totype galaxies, astronomers could not calibrate these relative studying Cepheid variables. The key project has now detected distance measurements. Thus, they were unable to make about 50 Cepheid variables in M100 and determined a distance accurate determinations of the Hubble constant. of 16.1 Ϯ 1.8 Mpc for the galaxy (10–12). Because M100 is Over the past few decades, leading astronomers, using close enough to us so that its peculiar motion (its motion different data sets, reported values for the Hubble constant induced by the gravitational influence of nearby mass con- that varied between 50 and 100 km͞s͞Mpc (5 ϫ 10Ϫ11 to 1 ϫ centrations) may be a significant fraction of its Hubble expan- 10Ϫ10 yrϪ1) with groups claiming errors as small as 5 km͞s͞ sion velocity, the key project team used relative distance Mpc (9). Resolving this discrepancy, which corresponds to a indicators to extrapolate from the Virgo cluster, a cluster

FIG. 4. M100, one of the spiral galaxies used in the Hubble constant key project analysis, as seen by prerepair (Left) and postrepair HST (image from HST Public Archive STScI-Pr94-01). (This figure was created with support from the Space Telescope Science Institute, operated by the Association of Universities for Research in Astronomy, Inc., from NASA contract NAS5-26555, and is reproduced with permission from AURA͞STScI.) Downloaded by guest on September 26, 2021 From the Academy: Spergel et al. Proc. Natl. Acad. Sci. USA 94 (1997) 6583

containing M100, to the more distant Coma cluster and to universe model. When Hubble’s study of nearby galaxies obtain a measurement of the Hubble constant: showed that the universe was expanding, Einstein regretted modifying his elegant theory and viewed the ⌳ term as his H0 ϭ 80 Ϯ 17 km͞s͞Mpc. ‘‘greatest mistake.’’ Many cosmologists advocate reviving the ⌳ term. Modern The dominant source of error is a result of the extended field theory associates this term with the energy density of the angular extent of the Virgo cluster on the sky and the uncer- vacuum.** For this term to be cosmologically interesting, its tainty of knowing where M100 lies with respect to the center value would need to be ϳ (10Ϫ4 eV)4 and would either require of the cluster. This error will be reduced when more distances new physics on the milli-eV scale or some minute (10Ϫ120) to Virgo cluster galaxies are obtained. correction to quantum gravity; either way, the addition of a The key project determination of the Hubble constant is term has profound implications for consistent with a number of independent efforts to estimate particle theory (15). the Hubble constant. A recent statistical synthesis (13) of the The advantage of the cosmological constant term is that it published literature yields 66 Ͻ H0 Ͻ 82 km͞s͞Mpc as a 95% significantly improves the agreement between theory and confidence interval. However, there still is not a complete observation (16, 17). If the cosmological constant today con- consensus on the value of the Hubble constant; a recent tributes most of the energy density of the universe, then the analysis using type Ia supernovae yields a value for the Hubble extrapolated age is much larger. Adding a cosmological con- constant that is formally inconsistent with many previous stant term to the inflationary model leads to a model that measurements: H0 ϭ 47 Ϯ 5km͞s͞Mpc (14). appears to be consistent with the observed large-scale distri- In the past year, the key project has detected Cepheids in bution of galaxies and clusters (18), measurements of cosmic eight other galaxies, and the results are consistent with those background fluctuations (19), and properties of x-ray clusters from M100. These new observations make possible a number (20). of important checks and calibrations. In M101, the key project The cosmological constant term alters the relationship has detected Cepheids in both metal-poor and metal-rich between distance and time. Specifically, for a positive value for 2 regions; this will enable a test to see if the Cepheid properties ⌳͞3H0, the volume of the universe and look-back time at a depend on abundances. A particularly important measurement given increases. One of the observational consequences is the determination of the distance to the Fornax cluster, a of this altered geometry is a much higher probability for nearby group of galaxies used to calibrate the supernova, in ‘‘multiple image gravitational lenses.’’ Multiple image gravi- addition to three other relative distance scales. This measure- tational lenses can arise when light traveling from a distant ment will be important for understanding the remaining quasar toward our telescopes passes through a galaxy or a discrepancies. Ultimately, the key project should be able to cluster of galaxies. The mass along the line of sight serves as make a reliable measurement of the Hubble constant that is a lens and can produce multiple images of the distant quasar. accurate to better than 10%. Turner (21) showed that the probability of multiple image gravitational lenses was much higher in a universe with a large Discussion and Implicationsʈ cosmological constant term. Thus, if ⌳ was large, the HST would show multiple images nearly every time it was used to The lower limit on the age of the universe can be combined observe a distant quasar. This was not seen in a ‘‘snapshot with the key project determination of the Hubble constant to survey’’ (22) or in large ground-based surveys (23). Based on yield a dimensionless number, this lack of lenses, Chris Kochanek, one of the panelists, has placed a 95% confidence level upper limit of ⍀⌳ Ͻ 0.66, which H0t0 ϭ 1.28 Ϯ 0.31. eliminates much of the ‘‘allowed parameter’’ space (24). If nonrelativistic matter makes up only 25% of the total mass Here, we optimistically set the age of the universe equal to of the universe, then the remaining ‘‘stuff’’ could be in some the age of the oldest stars, clearly an underestimate. If the new form. The cosmological constant is only one possible way universe is flat and matter-dominated, then theory predicts of modifying the equation of state of the universe. Other H t 2 3. This discrepancy does not yet have enormous 0 0 ϭ ͞ possibilities include non-Abelian gauged strings or a new form statistical significance and may reflect some unidentified set of matter. These exotic suggestions all have distinctive obser- of problems in either the theory of stellar evolution, the vational signatures that are testable in the next 5–10 years. cluster distance scale, or extragalactic distance scales. How- Is the Universe Open? Another possible solution to the age ever, it also may be the signature of missing physics in the big problem is abandoning the assumption that the universe is flat. bang theory. There is little observational evidence that the universe is flat, The determination of the age of the universe from the only theoretical prejudice. Hubble constant depends on the total density and on the If the universe is open and matter-dominated, then the composition of matter in the universe. The prediction that H0t0 predicted age for fixed Hubble constant is larger than a flat ϭ 2͞3 assumes that the universe was composed mostly of matter-dominated universe, but smaller than a flat universe ‘‘normal’’ nonrelativistic matter and that the density of the with a cosmological constant and the same matter content. The universe was sufficient to make its geometry flat (see Appendix Hubble constant predicts H0t0 ϳ 0.8 for cosmologically inter- for further discussion). By relaxing either of these assumptions, esting parameters. An open matter-dominated inflationary we alter the prediction for H0t0. model, like its cosmological constant-dominated cousin, ap- Cosmological Constant. Einstein first proposed the cosmo- pears to be consistent with the observed large-scale distribu- logical constant, ⌳, as a mathematical fix to the theory of tion of galaxies and clusters, measurements of cosmic back- general relativity. In its simplest form, the theory predicted ground fluctuations (25, 26), and properties of x-ray clusters that the universe must either expand or contract. Einstein (20). However, unlike the cosmological constant model, the thought the universe was static, so he added this new term to open matter-dominated model does not predict excessive stop the expansion. Friedman, a Russian mathematician, re- alized that this was an unstable fix and proposed an expanding **In the discussion, one member of the audience asked about Sidney Coleman’s work which suggested that quantum gravity effects would ʈThe discussion panel consisted of Michael Bolte, Wendy Freedman, set ⌳ϭ0. Glenn Starkman noted that Coleman’s calculation would Chris Kochanek (Harvard University), Mark Pinneassoult (Ohio also imply that the electron mass and its coupling to electromag- State University), and David Spergel. netism was also zero. Downloaded by guest on September 26, 2021 6584 From the Academy: Spergel et al. Proc. Natl. Acad. Sci. USA 94 (1997)

numbers of gravitational lenses. On the other hand, the range physics, and it can explain the large of the universe. As of Hubble’s constant and age consistent with the model is a bonus, the theory also provides a mechanism for generating smaller (25); the model requires H0 ϳ 60–65 km͞s͞Mpc and density fluctuations that can grow to form galaxies. t0 Ͻ 12 Gyr, marginally consistent with the observations If ⍀ϭ1 and the universe is composed primarily of matter, discussed earlier. then the big bang theory makes a definite prediction about the Future Observations. Observations in the next few years will product of the expansion rate of the universe, H0, and the age clarify the age problem and, perhaps, point to its resolution. of the universe, t0: Planned observations of nearby galaxies will cross-check the distance scale, reduce concerns about systematic errors, and 2 H0t0 ϭ . shrink the error bars on H0. Similarly, future observations of 3 binary systems and of nearby subdwarfs will further test stellar evolution models and increase confidence in determinations of This prediction can be altered if most of the mass density in the t0. universe is in some new form. Observations of the background will provide an independent probe of these basic parameters. Planned all-sky 1. Peebles, P. J. E., Schramm, D. N., Turner, E. L. & Kron, R. G. high-resolution maps of the microwave background will test (1991) Nature (London) 352, 769–776. the inflationary model and make independent measurements 2. Peebles, P. J. E., Schramm, D. N., Turner, E. L. & Kron, R. G. (1994) Sci. Am. 271, 29–33. of the Hubble constant, ⌳ and ⍀, potentially accurate to better 3. Bahcall, J. N. & Pinsonneault, M. M. (1992) Rev. Mod. Phys. 64, than 5% (27). For example (28), if the universe has a cosmo- 885–962. logical constant, the dominant scale for microwave back- 4. Bolte, M. & Hogan, C. J. (1995) Nature (London) 376, 399–402. ground fluctuations will be 1°, if it is open, the dominant scale 5. Hubble, E. P. (1924) Proc. Natl. Acad. Sci. USA 15, 168. will be 0.5°. Observations, not our theoretical prejudices, will 6. Freedman, W. L. & Madore, B. F. (1990) Astrophys. J. 365, resolve this issue. 186–194. 7. Jacoby, G., Branch, D., Ciardullo, R., Davies, R., Harris, W., Appendix: Age of the Universe in the Big Bang Theory Pierce, M., Pritchet, C., Tonry, J. & Welch, D. (1992) Publ. Astron. Soc. Pac. 104, 599–662. Astron. Astrophys. 54, If the universe is uniform, then general relativity has a simple 8. Tully, J. B. & Fisher, J. R. (1977) 661–673. 9. Sandage, A. & Tammann, G. A. (1993) Astrophys. J. 415, 1–9. solution for the evolution of the geometry of the universe: it 10. Freedman, W. L., Madore, B. F., Mould, J. R., Hill, R., Ferrar- either expands (or contracts) uniformly. The theory implies ese, L., Kennicutt, R. C., Saha, A., Stetson, P. B., Graham, J. 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