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A Younger Age for the Universe Straints (Table 1 and Fig R ESEARCH A RTICLES 66. The mean equatorial radius was derived from the tics for providing the engineering foundation that such a young age by such a wide array of harmonic model (65) based on a 1° sampling of an enabled this analysis. We also thank G. Elman, P. recent independent measurements. equatorial profile. This value is 200 m larger than was Jester, and J. Schott for assistance in altimetry pro- estimated from earlier data (5) but is within the error cessing, D. Rowlands and S. Fricke for help with orbit estimate of the earlier value. The uncertainty corre- determination, S. Zhong for assistance with the Hel- Method sponds to the standard error of the mean of the 360 las relaxation calculation, and G. McGill for a con- V Any measurement of a function of h, m, and equatorial samples. structive review. The MOLA investigation is support- V 67. We acknowledge the MOLA instrument team and the ed by the NASA Mars Global Surveyor Project. L can be included in a joint likelihood MGS spacecraft and operation teams at the Jet Pro- N pulsion Laboratory and Lockheed-Martin Astronau- 21 April 1999; accepted 10 May 1999 ~ V V ! 5 P L h, m, L Li (1) i51 which I take as the product of seven of the most recent independent cosmological con- A Younger Age for the Universe straints (Table 1 and Fig. 3). For example, one of the Li in Eq. 1 represents the con- Charles H. Lineweaver straints on h. Recent measurements can be summarized as h# 5 0.68 6 0.10 (16). I The age of the universe in the Big Bang model can be calculated from three represent these measurements in Eq. 1 by the V likelihood parameters: Hubble’s constant, h; the mass density of the universe, m; and the V # 2 cosmological constant, L. Recent observations of the cosmic microwave h 2 h ~ ! 5 F2 S D G background and six other cosmological measurements reduce the uncertainty LHubble h exp 0.5 6 0.10 in these three parameters, yielding an age for the universe of 13.4 1.6 billion (2) years, which is a billion years younger than other recent age estimates. A different standard Big Bang model, which includes cold dark matter with a Another Li in Eq. 1 comes from measure- cosmological constant, provides a consistent and absolutely time-calibrated ments of the fraction of normal baryonic evolutionary sequence for the universe. matter in clusters of galaxies (14) and esti- mates of the density of normal baryonic mat- V 2 5 6 In the Big Bang model, the age of the uni- ments with SNe and other data, I (9) have ter in the universe [ bh 0.015 0.005 V 5 6 verse, to, is a function of three parameters: h, reported L 0.62 0.16 [see (10–12) for (15, 18)]. When combined, these measure- V V V Þ V 2/3 5 6 m, and L (1). The dimensionless Hubble similar results]. If L 0, then estimates of the ments yield mh 0.19 0.12 (19), constant, h, tells us how fast the universe is age of the universe in Big Bang models must which contributes to the likelihood through V expanding. The density of matter in the uni- include L. Thus, one must use the most gen- ~ V ! Lbaryons h, m verse, V , slows the expansion, and the cos- eral form: t 5 f(V , V )/h (13). m o m L V 2/3 2 V 2/3 2 V mh mh mological constant, L, speeds up the expan- Here, I have combined recent independent 5 expF20.5S D G sion (Fig. 1). measurements of CMB anisotropies (9), type Ia 0.12 Until recently, large uncertainties in the SNe (4, 5), cluster mass-to-light ratios (6), clus- (3) V V V V measurements of h, m, and L made efforts ter abundance evolution (7), cluster baryonic The ( m, L)–dependencies of the remain- V V to determine to (h, m, L) unreliable. The- fractions (14), deuterium-to-hydrogen ratios in ing five constraints are plotted in Fig. 3 (20). oretical preferences were, and still are, often quasar spectra (15), double-lobed radio sources The 68% confidence level regions derived used to remedy these observational uncertain- (8), and the Hubble constant (16) to determine from CMB and SNe (Fig. 3, A and B) are V 5 ties. One assumed the standard model ( m the age of the universe. The big picture from the nearly orthogonal, and the region of overlap 1, VL 5 0), dating the age of the universe to analysis done here is as follows (Figs. 1 and 2): is relatively small. Similar complementarity 5 ; to 6.52/h billion years old (Ga). However, The Big Bang occurred at 13.4 Ga. About 1.2 exists between the CMB and the other data for large or even moderate h estimates billion years (Gy) later, the halo of our Galaxy sets (Fig. 3, C through E). The combination ()0.65), these simplifying assumptions re- (and presumably the halo of other galaxies) of them all (Fig. 3F) yields VL 5 0.65 6 V 5 6 sulted in an age crisis in which the universe formed. About 3.5 Gy later, the disk of our 0.13 and m 0.23 0.08 (21). ' , was younger than our Galaxy (to 10 Ga Galaxy (and presumably the disks of other This complementarity is even more im- ' tGal 12 Ga). These assumptions also result- spiral galaxies) formed. This picture agrees portant (but more difficult to visualize) in V ed in a baryon crisis in which estimates of the with what we know about galaxy forma- three-dimensional parameter space, (h, m, amount of normal (baryonic) matter in the tion. Even the recent indications of the VL). Although the CMB alone cannot tightly universe were in conflict (2, 3). existence of old galaxies at high redshift constrain any of these parameters, it does V , Evidence in favor of m 1 has become (17) fit into the time framework determined have a strong preference in the three-dimen- V V V more compelling (4–8), but L is still often here. In this sense, the result is not surpris- sional space (h, m, L). In Eq. 1, I used V V assumed to be zero, not because it is measured ing. What is new is the support given to LCMB(h, m, L), which is a generalization to be so, but because models are simpler with- out it. Recent evidence from supernovae (SNe) (4, 5) indicates that V . 0. These SNe data Table 1. Parameter estimates from non-CMB measurements. I refer to these as constraints. I use the error L bars cited here as 1s errors in the likelihood analysis. The first four constraints are plotted in Fig. 3, B and other data exclude the standard Einstein- through E. V 5 V 5 deSitter model ( m 1, L 0). The cosmic microwave background (CMB), on the other Method Reference Estimate V V 5 hand, excludes models with low m and L V V VL50 52 6 Vflat 5 6 0(3). With both high and low m excluded, L SNe (35) m 0.28 0.16, m 0.27 0.14 VL50 5 6 cannot be zero. Combining CMB measure- Cluster mass-to-light (6) m 0.19 0.14 VL50 5 10.28 Vflat 5 10.25 Cluster abundance evolution (7) m 0.1720.10 , m 0.2220.10 VL50 52 10.70 Vflat 5 10.50 Double radio sources (8) m 0.2520.50 , m 0.120.20 V 2/3 5 6 School of Physics, University of New South Wales, Baryons (19) mh 0.19 0.12 Sydney NSW 2052, Australia. E-mail: charley@bat. Hubble (16) h 5 0.68 6 0.10 phys.unsw.edu.au www.sciencemag.org SCIENCE VOL 284 28 MAY 1999 1503 R ESEARCH A RTICLES V V 5 6 of LCMB( m, L) (Fig. 3A) (22). To convert h 0.68 0.10 but does not depend strongly age, independent of the SNe and CMB data, V 2 2 5 13.4 the three-dimensional likelihood L(h, m, on the central value assumed for Hubble’s con- is to(all CMB SNe) 12.622.0 Ga, VL) of Eq. 1 into an estimate of the age of the stant (as long as this central value is in the most which is somewhat lower than the main result universe and into a more easily visualized accepted range, 0.64 # h # 0.72) or on the but within the error bars. two-dimensional likelihood, L(h, to), I com- uncertainty of h (unless this uncertainty is taken puted the dynamic age corresponding to each to be very small). Assuming an uncertainty of The Oldest Objects in Our Galaxy V 5 point in the three-dimensional space (h, m, 0.10, age estimates from using h 0.64, 0.68, The universe cannot be younger than the oldest V L). For a given h and to, I then set L(h, to) and 0.72 are 13.5, 13.4, and 13.3 Ga, respec- objects in it. Thus, estimates of the age of the V V equal to the maximum value of L(h, m, L) tively (Fig. 2). Using a larger uncertainty of oldest objects in our Galaxy are lower limits to 0.15 with the same h values does not substan- the age of the universe (Table 2 and Fig.
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