The Expanding Universe PDF

1502 CHAPTER 44 Particle Physics and Cosmology 44.15 This photo shows the interior of the In the standard model, the neutrinos have zero mass. Nonzero values are con- Super-Kamiokande neutrino detector in troversial because experiments to determine neutrino...

1502 CHAPTER 44 Particle Physics and Cosmology 44.15 This photo shows the interior of the In the standard model, the neutrinos have zero mass. Nonzero values are con- Super-Kamiokande neutrino detector in troversial because experiments to determine neutrino masses are difficult both to Japan. When in operation, the detector is perform and to analyze. In most GUTs the neutrinos must have nonzero masses. filled with 5 * 107 kg of water. A neutrino passing through the detector can produce a If neutrinos do have mass, transitions called neutrino oscillations can occur, in faint flash of light, which is detected by which one type of neutrino (ne , nm, or nt) changes into another type. In 1998, the 13,000 photomultiplier tubes lining the scientists using the Super-Kamiokande neutrino detector in Japan (Fig. 44.15) detector walls. Data from this detector reported the discovery of oscillations between muon neutrinos and tau neutrinos. were the first to indicate that neutrinos Subsequent measurements at the Sudbury Neutrino Observatory in Canada have have mass. confirmed the existence of neutrino oscillations. This discovery is evidence for exciting physics beyond that predicted by the standard model. The discovery of neutrino oscillations cleared up a long-standing mystery. Since the 1960s, physicists have been using sensitive detectors to look for electron neutrinos produced by nuclear fusion reactions in the sun’s core (see Section 43.8). However, the observed flux of solar electron neutrinos is only one-third of the predicted value. The explanation was provided in 2002 by the Sudbury Neutrino Observatory, which can detect neutrinos of all three flavors. The results showed that the combined flux of solar neutrinos of all flavors is equal to the theoretical prediction for the flux of electron neutrinos. The explanation is that the sun is producing electron neutrinos at the predicted rate, but that two-thirds of these electron neutrinos are transformed into muon or tau neutrinos during their flight from the sun’s core to a detector on earth. Supersymmetric Theories and TOEs The ultimate dream of theorists is to unify all four fundamental interactions, adding gravitation to the strong and electroweak interactions that are included in GUTs. Such a unified theory is whimsically called a Theory of Everything (TOE). It turns out that an essential ingredient of such theories is a space-time continuum with more than four dimensions. The additional dimensions are “rolled up” into extremely tiny structures that we ordinarily do not notice. Depending on the scale of these structures, it may be possible for the next generation of particle accelerators to reveal the presence of extra dimensions. Another ingredient of many theories is supersymmetry, which gives every boson and fermion a “superpartner” of the other spin type. For example, the proposed supersymmetric partner of the spin@12 electron is a spin-0 particle called the selectron, and that of the spin-1 photon is a spin@12 photino. As yet, no super- partner particles have been discovered, perhaps because they are too massive to be produced by the present generation of accelerators. Within a few years, new data from the Large Hadron Collider will help us decide whether these intriguing theories have merit. TEST YOUR UNDERSTANDING OF SECTION 44.5 One aspect of the standard model is that a d quark can transform into a u quark, an electron, and an antineutrino by means of the weak interaction. If this happens to a d quark inside a neutron, what kind of particle remains afterward in addition to the electron and antineutrino? (i) A proton; (ii) a Σ -; (iii) a Σ +; (iv) a Λ0 or a Σ 0; (v) any of these. ❙ 44.6 THE EXPANDING UNIVERSE In the last two sections of this chapter we’ll explore briefly the connections between the early history of the universe and the interactions of fundamental particles. It is remarkable that there are such close ties between physics on the smallest scale that we’ve explored experimentally (the range of the weak interac- tion, of the order of 10-18 m) and physics on the largest scale (the universe itself, of the order of at least 1026 m). M44_YOUN3610_14_SE_C44_1481-1522.indd 1502 15/10/14 10:38 AM  44.6 The Expanding Universe 1503 Gravitational interactions play an essential role in the large-scale behavior of 44.16 (a) The galaxy M101 is a larger the universe. We saw in Chapter 13 how the law of gravitation explains the motions version of the Milky Way galaxy of which our solar system is a part. Like all galaxies, of planets in the solar system. Astronomical evidence shows that gravitational M101 is held together by the mutual forces also dominate in larger systems such as galaxies and clusters of galaxies gravitational attraction of its stars, gas, (Fig. 44.16). dust, and other matter, all of which orbit Until early in the 20th century it was usually assumed that the universe was around the galaxy’s center of mass. M101 static; stars might move relative to each other, but there was not thought to be is 25 million light-years away. (b) This image shows part of the Coma cluster, an any overall expansion or contraction. But measurements that were begun in 1912 immense grouping of over 1000 galaxies by Vesto Slipher at Lowell Observatory in Arizona, and continued in the 1920s by that lies 300 million light-years from us. Edwin Hubble with the help of Milton Humason at Mount Wilson in California, The galaxies within the cluster are all in indicated that the universe is not static. The motions of galaxies relative to the motion. Gravitational forces between the earth can be measured by observing the shifts in the wavelengths of their spectra. galaxies prevent them from escaping from the cluster. For distant galaxies these shifts are always toward longer wavelength, so they appear to be receding from us and from each other. Astronomers first assumed (a) that these were Doppler shifts and used a relationship between the wavelength l0 of light measured now on earth from a source receding at speed v and the wave- length lS measured in the rest frame of the source when it was emitted. We can derive this relationship by inverting Eq. (37.25) for the Doppler effect, making subscript changes, and using l = c>f ; the result is c + v l0 = lS (44.13) Ac - v Wavelengths from receding sources are always shifted toward longer wave- lengths; this increase in l is called the redshift. We can solve Eq. (44.13) for v: (b) 1l0>lS22 - 1 v = c (44.14) 1l0>lS22 + 1 CAUTION Redshift, not Doppler shift Equations (44.13) and (44.14) are from the special theory of relativity and refer to the Doppler effect. As we’ll see, the redshift from distant galaxies is caused by an effect that is explained by the general theory of relativity and is not a Doppler shift. However, as the ratio v>c and the fractional wavelength change 1l0 - lS2>lS become small, the general theory’s equations approach Eqs. (44.13) and (44.14), and those equations may be used. ❙ SOLUTION EXAMPLE 44.8 RECESSION SPEED OF A GALAXY The spectral lines of various elements are detected in light from EXECUTE: The fractional wavelength redshift for this galaxy a galaxy in the constellation Ursa Major. An ultraviolet line from is l0>lS = 1414 nm2>1393 nm2 = 1.053. This is only a 5.3% singly ionized calcium 1lS = 393 nm2 is observed at wavelength increase, so we can use Eq. (44.14) with reasonable accuracy: l0 = 414 nm, redshifted into the visible portion of the spectrum. 11.05322 - 1 At what speed is this galaxy receding from us? v = c = 0.0516c = 1.55 * 107 m>s 11.05322 + 1 SOLUTION EVALUATE: The galaxy is receding from the earth at 5.16% of IDENTIFY and SET UP: This example uses the relationship between the speed of light. Rather than going through this calculation, redshift and recession speed for a distant galaxy. We can use the astronomers often just state the redshift z = 1l0 - lS2>lS = wavelengths lS at which the light is emitted and l0 that we detect 1l0>lS2 - 1. This galaxy has redshift z = 0.053. on earth in Eq. (44.14) to determine the galaxy’s recession speed v if the fractional wavelength shift is not too great. M44_YOUN3610_14_SE_C44_1481-1522.indd 1503 15/10/14 10:38 AM  1504 CHAPTER 44 Particle Physics and Cosmology 44.17 Graph of recession speed versus The Hubble Law distance for several galaxies. The best-fit straight line illustrates Hubble’s law. The Analysis of redshifts from many distant galaxies led Edwin Hubble to a remark- slope of the line is the Hubble constant, H0. able conclusion: The speed of recession v of a galaxy is proportional to its dis- v (103 km>s) tance r from us (Fig. 44.17). This relationship is now called the Hubble law; expressed as an equation, 20 v = H0 r (44.15) 15 where H0 is an experimental quantity commonly called the Hubble constant, 10 since at any given time it is constant over space. Determining H0 has been a key Slope = H0 5 goal of the Hubble Space Telescope, which can measure distances to galaxies with unprecedented accuracy. The current best value is 2.18 * 10-18 s-1, with 0 100 200 300 an uncertainty of 2%. r (megaparsecs) Astronomical distances are often measured in parsecs (pc); one parsec is the distance at which there is a one-arcsecond 11>3600°2 angular separation between two objects 1.50 * 1011 m apart (the average distance from the earth to the sun). A distance of 1 pc is equal to 3.26 light-years (ly), where 1 ly = 9.46 * 1012 km is the distance that light travels in one year. The Hubble constant is then com- monly expressed in the mixed units 1km>s2>Mpc (kilometers per second per megaparsec), where 1 Mpc = 106 pc: 9.46 * 1012 km 3.26 ly 106 pc km>s H0 = 12.18 * 10-18 s-12 a ba ba b = 67.3 1 ly 1 pc 1 Mpc Mpc SOLUTION EXAMPLE 44.9 DETERMINING DISTANCE WITH THE HUBBLE LAW Use the Hubble law to find the distance from earth to the galaxy in EVALUATE: A distance of 230 million parsecs (750 million light- Ursa Major described in Example 44.8. years) is truly stupendous, but many galaxies lie much farther away. To appreciate the immensity of this distance, consider that SOLUTION our farthest-ranging unmanned spacecraft have traveled only about 0.002 ly from our planet. IDENTIFY and SET UP: The Hubble law relates the redshift of a distant galaxy to its distance r from earth. We solve Eq. (44.15) for r and substitute the recession speed v from Example 44.8. EXECUTE: Using H0 = 67.3 1km>s2>Mpc = 6.73 * 104 1m>s2>Mpc, v 1.55 * 107 m>s r = = = 230 Mpc H0 6.73 * 104 1m>s2>Mpc = 2.3 * 108 pc = 7.5 * 108 ly = 7.1 * 1024 m Another aspect of Hubble’s observations was that, in all directions, distant galaxies appeared to be receding from us. There is no particular reason to think that our galaxy is at the very center of the universe; if we lived in some other galaxy, every distant galaxy would still seem to be moving away. That is, at any given time, the universe looks more or less the same, no matter where in the universe we are. This important idea is called the cosmological principle. There are local fluctuations in density, but on average, the universe looks the same from all locations. Thus the Hubble constant is constant in space although not neces- sarily constant in time, and the laws of physics are the same everywhere. The Big Bang The Hubble law suggests that at some time in the past, all the matter in the uni- verse was far more concentrated than it is today. It was then blown apart in a rapid expansion called the Big Bang, giving all observable matter more or less the velocities that we observe today. When did this happen? According to the M44_YOUN3610_14_SE_C44_1481-1522.indd 1504 15/10/14 10:38 AM  44.6 The Expanding Universe 1505 Hubble law, matter at a distance r away from us is traveling with speed v = H0 r. The time t needed to travel a distance r is r r 1 t = = = = 4.59 * 1017 s = 1.45 * 1010 y v H0 r H0 By this hypothesis the Big Bang occurred about 14 billion years ago. It assumes that all speeds are constant after the Big Bang; that is, it ignores any change in the expansion rate due to gravitational attraction or other effects. We’ll return to this point later. For now, however, notice that the age of the earth determined from radioactive dating (see Section 43.4) is 4.54 billion 14.54 * 1092 years. It’s encouraging that our hypothesis tells us that the universe is older than the earth! Expanding Space The general theory of relativity takes a radically different view of the expansion just described. According to this theory, the increased wavelength is not caused by a Doppler shift as the universe expands into a previously empty void. Rather, the increase comes from the expansion of space itself and everything in inter- galactic space, including the wavelengths of light traveling to us from distant sources. This is not an easy concept to grasp, and if you haven’t encountered it before, it may sound like doubletalk. An analogy may help you develop some intuition on this point. Imagine we are all bugs crawling around on a horizontal surface. We can’t leave the surface, 44.18 An inflating balloon as an analogy and we can see in any direction along the surface, but not up or down. We are for an expanding universe. then living in a two-dimensional world; some writers have called such a world (a) Points (representing galaxies) on the flatland. If the surface is a plane, we can locate our position with two Cartesian surface of a balloon are described by their latitude and longitude coordinates. coordinates 1x, y2. If the plane extends indefinitely in both the x- and y@directions, we described our space as having infinite extent, or as being unbounded. No matter how far we go, we never reach an edge or a boundary. R An alternative habitat for us bugs would be the surface of a sphere of radius R. R The space would still seem infinite—we could crawl forever and never reach an edge or a boundary. Yet in this case the space is finite or bounded. To describe the location of a point in this space, we could still use two coordinates: latitude and longitude, or the spherical coordinates u and f shown in Fig. 41.5. Now suppose the spherical surface is that of a balloon (Fig. 44.18). As we inflate the balloon more and more, increasing the radius R, the coordinates of a point don’t change, yet the distance between any two points gets larger and larger. Furthermore, as R increases, the rate of change of distance between two points (their recession speed) is proportional to their distance apart. The recession (b) The radius R of the balloon has increased. speed is proportional to the distance, just as with the Hubble law. For example, The coordinates of the points are the same, but the distance from Pittsburgh to Miami is twice as great as the distance from the distance between them has increased. Pittsburgh to Boston. If the earth were to begin to swell, Miami would recede from Pittsburgh twice as fast as Boston would. Although the quantity R isn’t one of the two coordinates giving the position of a point on the balloon’s surface, it nevertheless plays an essential role in any dis- R cussion of distance. It is the radius of curvature of our two-dimensional universe, and it is also a varying scale factor that changes as this universe expands. R Generalizing this picture to three dimensions isn’t so easy. We have to think of our three-dimensional space as being embedded in a space with four or more dimensions, just as we visualized the two-dimensional spherical flatland as being embedded in a three-dimensional Cartesian space. Our real three-space is not Cartesian; to describe its characteristics in any small region requires at least one The rate of recession additional parameter, the curvature of space, which is analogous to the radius of for any two points is the sphere. In a sense, this scale factor, which we’ll continue to call R, describes proportional to the the size of the universe, just as the radius of the sphere described the size distance between them. of our two-dimensional spherical universe. We’ll return later to the question of whether the universe is bounded or unbounded. M44_YOUN3610_14_SE_C44_1481-1522.indd 1505 25/10/14 11:30 AM  1506 CHAPTER 44 Particle Physics and Cosmology Any length that is measured in intergalactic space is proportional to R, so the wavelength of light traveling to us from a distant galaxy increases along with every other dimension as the universe expands. That is, l0 R0 = (44.16) l R The zero subscripts refer to the values of the wavelength and scale factor now, just as H0 is the current value of the Hubble constant. The quantities l and R without subscripts are the values at any time—past, present, or future. For the galaxy described in Examples 44.8 and 44.9, we have l0 = 414 nm and l = lS = 393 nm, so Eq. (44.16) gives R0>R = 1.053. That is, the scale factor now 1R02 is 5.3% larger than it was 750 million years ago when the light was emitted from that galaxy in Ursa Major. This increase of wavelength with time as the scale factor increases in our expanding universe is called the cosmological redshift. The farther away an object is, the longer its light takes to get to us and the greater the change in R and l. The current largest measured wavelength ratio for galaxies is about 8.6, meaning that the volume of space itself is about 18.623 ≈ 640 times larger than it was when the light was emitted. Do not attempt to substitute l0>lS = 8.6 into Eq. (44.14) to find the recession speed; that equation is accurate only for small cosmological redshifts and v V c. The actual value of v depends on the density of the universe, the value of H0 , and the expansion history of the universe. Here’s a surprise: If the distance from us in the Hubble law is large enough, then the speed of recession is greater than the speed of light! This does not violate the special theory of relativity because the recession speed is not caused by the motion of the astronomical object relative to some coordinates in its region of space. Rather, v 7 c when two sets of coordinates move apart fast enough as space itself expands. In other words, there are objects whose coordinates have been moving away from our coordinates so fast that light from them hasn’t had enough time in the entire history of the universe to reach us. What we see is just the observable universe; we have no direct evidence about what lies beyond its horizon. CAUTION The universe isn’t expanding into emptiness The balloon shown in Fig. 44.18 is expanding into the empty space around it. It’s a common misconception to picture the universe in the same way as a large but finite collection of galaxies that’s expanding into unoccupied space. The reality is quite different! All evidence shows that our universe is infinite: It has no edges, so there is nothing “outside” it and it isn’t “expanding into” any- thing. The expansion of the universe simply means that the scale factor of the universe is increasing. A good two-dimensional analogy is to think of the universe as a flat, infinitely large rubber sheet that’s stretching and expanding much like the surface of the balloon in Fig. 44.18. In a sense, the infinite universe is becoming more infinite! ❙ Critical Density In an expanding universe, gravitational attractions between galaxies should slow the initial expansion. But by how much? If these attractions are strong enough, the universe should expand more and more slowly, eventually stop, and then begin to contract, perhaps all the way down to what’s been called a Big Crunch. On the other hand, if gravitational forces are much weaker, they slow the expan- sion only a little, and the universe should continue to expand forever. The situation is analogous to the problem of escape speed of a projectile launched from the earth. We studied this problem in Example 13.5 (Section 13.3). The total energy E = K + U when a projectile of mass m and speed v is at a distance r from the center of the earth (mass m E) is Gmm E E = 12 mv 2 - r M44_YOUN3610_14_SE_C44_1481-1522.indd 1506 15/10/14 10:38 AM  44.6 The Expanding Universe 1507 If E is positive, the projectile has enough kinetic energy to move infinitely far from the earth 1r S q2 and have some kinetic energy left over. If E is nega- tive, the kinetic energy K = 12 mv 2 becomes zero and the projectile stops when r = -Gmm E >E. In that case, no greater value of r is possible, and the projectile can’t escape the earth’s gravity. We can carry out a similar analysis for the universe. Whether the universe continues to expand indefinitely should depend on the average density of matter. If matter is relatively dense, there is a lot of gravitational attraction to slow and eventually stop the expansion and make the universe contract again. If not, the expansion should continue indefinitely. We can derive an expression for the critical density rc needed to just barely stop the expansion. Here’s a calculation based on Newtonian mechanics; it isn’t relativistically 44.19 An imaginary sphere of galaxies. correct, but it illustrates the idea. Consider a large sphere with radius R, contain- The net gravitational force exerted on our galaxy (at the surface of the sphere) by the ing many galaxies (Fig. 44.19), with total mass M. Suppose our own galaxy has other galaxies is the same as if all of their mass m and is located at the surface of this sphere. According to the cosmological mass were concentrated at the center of the principle, the average distribution of matter within the sphere is uniform. The sphere. (Since the universe is infinite, total gravitational force on our galaxy is just the force due to the mass M inside there’s also an infinity of galaxies outside the sphere. The force on our galaxy and potential energy U due to this spherically this sphere.) v symmetric distribution are the same as though m and M were both points, so U = -GmM>R, just as in Section 13.3. The net force from all the uniform distri- bution of mass outside the sphere is zero, so we’ll ignore it. The total energy E (kinetic plus potential) for our galaxy is Sphere of galaxies, v total mass M v 1 2 GmM E = 2 mv - (44.17) R Radius R If E is positive, our galaxy has enough energy to escape from the gravitational Our galaxy, attraction of the mass M inside the sphere; in this case the universe should keep v mass m expanding forever. If E is negative, our galaxy cannot escape and the universe should eventually pull back together. The crossover between these two cases occurs when E = 0, so 1 2 GmM 2 mv = (44.18) R The total mass M inside the sphere is the volume 4pR3>3 times the density rc : M = 43 pR3rc We’ll assume that the speed v of our galaxy relative to the center of the sphere is given by the Hubble law: v = H0R. Substituting these expressions for m and v into Eq. (44.18), we get Gm 4 3 1 2 m1H0 R2 2 = 1 pR rc 2 or R 3 3H 02 rc = (critical density of the universe) (44.19) 8pG This is the critical density. If the average density is less than rc , the universe should continue to expand indefinitely; if it is greater, the universe should even- tually stop expanding and begin to contract. Putting numbers into Eq. (44.19), we find 312.18 * 10-18 s-122 rc = = 8.50 * 10-27 kg>m3 8p16.67 * 10-11 N # m2>kg 22 The mass of a hydrogen atom is 1.67 * 10-27 kg, so this density is equivalent to about five hydrogen atoms per cubic meter. M44_YOUN3610_14_SE_C44_1481-1522.indd 1507 15/10/14 10:38 AM  1508 CHAPTER 44 Particle Physics and Cosmology Dark Matter, Dark Energy, and the Accelerating Universe Astronomers have made extensive studies of the average density of matter in the universe. One way to do so is to count the number of galaxies in a patch of sky. Based on the mass of an average star and the number of stars in an average galaxy, this effort gives an estimate of the average density of luminous matter in the universe—that is, matter that emits electromagnetic radiation. (You are made of luminous matter because you emit infrared radiation as a consequence of your temperature; see Sections 17.7 and 39.5.) It’s also necessary to take into account other luminous matter within a galaxy, including the tenuous gas and dust between the stars. Another technique is to study the motions of galaxies within clusters of galax- ies (see Fig. 44.16b). The motions are so slow that we can’t actually see galaxies changing positions within a cluster. However, observations show that different galaxies within a cluster have somewhat different redshifts, which indicates that the galaxies are moving relative to the center of mass of the cluster. The speeds of these motions are related to the gravitational force exerted on each galaxy by the other members of the cluster, which in turn depends on the total mass of the cluster. By measuring these speeds, astronomers can determine the average density of all kinds of matter within the cluster, whether or not the matter emits electromagnetic radiation. Observations using these and other techniques show that the average density of all matter in the universe is 31.5% of the critical density, but the average den- sity of luminous matter is only 4.9% of the critical density. In other words, most of the matter in the universe is not luminous: It does not emit electromagnetic radiation of any kind. At present, the nature of this dark matter remains an outstanding mystery. Some proposed candidates for dark matter are WIMPs (weakly interacting massive particles, which are hypothetical subatomic particles far more massive than those produced in accelerator experiments) and MACHOs (massive compact halo objects, which include objects such as black holes that might form “halos” around galaxies). Whatever the true nature of dark matter, it is by far the dominant form of matter in the universe. For every kilogram of the conventional matter that has been our subject for most of this book—including 44.20 The bright spots in this image are not stars but entire galaxies. We see the electrons, protons, atoms, molecules, blocks on inclined planes, planets, and stars— most distant of these, magnified in the there are about five and a half kilograms of dark matter. inset, as it was 13.1 billion years ago, when Since the average density of matter in the universe is less than the critical the universe was just 700 million years old. density, it might seem fair to conclude that the universe will continue to expand At that time the scale factor of the universe indefinitely, and that gravitational attraction between matter in different parts was only about 12% as large as it is now. (The red color of this galaxy is due to its of the universe should slow the expansion down (albeit not enough to stop it). very large redshift.) By comparison, we One way to test this prediction is to examine the redshifts of extremely distant see the relatively nearby Coma cluster (see objects. The more distant a galaxy is, the more time it takes that light to reach Fig. 44.16b) as it was 300 million years us from that galaxy, so the further back in time we look when we observe that ago, when the scale factor was 98% of the galaxy. If the expansion of the universe has been slowing down, the expansion present-day value. must have been more rapid in the distant past. Thus we would expect very A very distant galaxy... distant galaxies to have greater redshifts than predicted by the Hubble law, Eq. (44.15). Only since the 1990s has it become possible to measure accurately both the distances and the redshifts of extremely distant galaxies. The results have been totally surprising: Very distant galaxies, seen as they were when the universe was a small fraction of its present age (Fig. 44.20), have smaller redshifts than predicted by the Hubble law! The implication is that the expansion of the universe was slower in the past than it is now, so the expansion has been speeding up rather than slowing down.... shown in close-up If gravitational attraction should make the expansion slow down, why is it speeding up instead? Our best explanation is that space is suffused with a kind of energy that has no gravitational effect and emits no electromagnetic radiation, M44_YOUN3610_14_SE_C44_1481-1522.indd 1508 15/10/14 10:38 AM  44.7 The Beginning of Time 1509 but rather acts as a kind of “antigravity” that produces a universal repulsion. This invisible, immaterial energy is called dark energy. As the name suggests, the nature of dark energy is poorly understood but is the subject of very active research. Observations show that the energy density of dark energy (measured in, say, joules per cubic meter) is 68.5% of the critical density times c2; that is, it is equal to 0.685rcc2. As described above, the average density of matter of all kinds is 31.5% of the critical density. From the Einstein relationship E = mc2, the aver- age energy density of matter in the universe is therefore 0.315rc c2. Because the energy density of dark energy is nearly three times greater than that of matter, the expansion of the universe will continue to accelerate. This expansion will never stop, and the universe will never contract. If we account for energy of all kinds, the average energy density of the ? 44.21 The composition of our universe. universe is equal to 0.685rcc2 + 0.315rcc2 = 1.00rcc2. Of this, 68.5% is Conventional matter includes all of the familiar sorts of matter that you see the mysterious dark energy, 26.6% is the no less mysterious dark matter, and a around you, including your body, our mere 4.9% is well-understood conventional matter. How little we know about planet, and the sun and stars. the contents of our universe (Fig. 44.21)! When we take account of the density Conventional matter: 4.9% of matter in the universe (which tends to slow the expansion of space) and the density of dark energy (which tends to speed up the expansion), the age of the universe turns out to be 13.8 billion 11.38 * 10102 years. What is the significance of the result that within observational error, the aver- age energy density of the universe is equal to rc c2? It tells us that the universe Dark matter: is infinite and unbounded, but just barely so. If the average energy density were 26.6% even slightly larger than rc c2, the universe would be finite like the surface of the balloon depicted in Fig. 44.18. As of this writing, the observational error in the average energy density is less than 1%, but we can’t be totally sure that the Dark energy: 68.5% universe is unbounded. Improving these measurements will be an important task for physicists and astronomers in the years ahead. TEST YOUR UNDERSTANDING OF SECTION 44.6 Is it accurate to say that your body is made of “ordinary” matter? ❙ BIO Application A Fossil Both Ancient and Recent This fossil trilobite is an example of a group of marine arthropods 44.7 THE BEGINNING OF TIME that flourished in earth’s oceans from 540 to 250 million years ago. (By comparison, the What an odd title for the very last section of a book! We will describe in general first dinosaurs did not appear until 230 million years ago.) From our perspective, this makes terms some of the current theories about the very early history of the universe trilobites almost unfathomably ancient. But and their relationship to fundamental particle interactions. We’ll find that an compared to the time that has elapsed since astonishing amount happened in the very first second. the Big Bang, 13.8 billion years, even trilobites are a very recent phenomenon: They first appeared when the universe was already 96% Temperatures of its present age. The early universe was extremely dense and extremely hot, and the average particle energies were extremely large, all many orders of magnitude beyond anything that exists in the present universe. We can compare particle energy E and absolute temperature T by using the equipartition principle (see Section 18.4): E = 32 kT (44.20) In this equation k is Boltzmann’s constant, which we’ll often express in eV>K: k = 8.617 * 10-5 eV>K Thus we can replace Eq. (44.20) by E ≈ 110-4 eV>K2T = 110-13 GeV>K2T when we’re discussing orders of magnitude. M44_YOUN3610_14_SE_C44_1481-1522.indd 1509 15/10/14 10:38 AM