Chapter 26

Chapter 26 Cosmology This image—called the Ultra Deep Field—was taken with the Advanced Camera for Surveys aboard the Hubble telescope. It is one of the finest photographs of deep space ever made. More than a thousand galaxies are crowded into this one image, displaying many different types, shapes, and colors. In all, astronomers estimate that the observable universe contains about 100 billion such galaxies. (NASA/ESA)

Units of Chapter 26 26.1 The Universe on the Largest Scales 26.2 The Expanding Universe 26.3 The Fate of the Cosmos 26.4 The Geometry of Space More Precisely 26-1 Curved Space 26.5 Will the Universe Expand Forever?

Units of Chapter 26 (cont.) 26.6 Dark Energy and Cosmology Discovery 26-1 Einstein and the Cosmological Constant 26.7 Cosmic Microwave Background

26.1 The Universe on the Largest Scales This galaxy map shows the largest structure known in the universe, the Sloan Great Wall. No structure larger than 300 Mpc is seen. Figure 26-1. Galaxy Survey This map of the universe is drawn using data from the Sloan Digital Sky Survey. (Discovery 25-1) It shows the locations of 66,976 galaxies lying within 12° of the celestial equator and extending to a distance of almost 1000 Mpc. The largest known structure in the universe, the Sloan Great Wall, is marked, stretching nearly 300 Mpc across the center of the frame. There is no evidence for any structure on larger scales. (SDSS)

26.1 The Universe on the Largest Scales This pencil-beam survey is another measure of large-scale structure. Again, there is structure at about 200–300 Mpc, but nothing larger. Figure 26-2. Pencil-Beam Survey The results of a deep “pencil-beam” survey of two small portions of the sky in opposite directions from Earth, perpendicular to the Galactic plane (a), are plotted in (b). The graph shows the number of galaxies found at different distances from us, out to about 2000 Mpc. Wherever we look on the sky, the distinctive “picket fence” pattern highlights voids and sheets of galaxies on scales of 100–200 Mpc, but gives no indication of any larger structures.

26.1 The Universe on the Largest Scales Therefore, the universe is homogenous (any 300-Mpc-square block appears much like any other) on scales greater than about 300 Mpc. The universe also appears to be isotropic—the same in all directions. The cosmological principle includes the assumptions of isotropy and homogeneity.

26.2 The Expanding Universe Olbers’s Paradox: If the universe is homogeneous, isotropic, infinite, and unchanging, the entire sky should be as bright as the surface of the Sun. Figure 26-3. Olbers’s Paradox If the universe were homogeneous, isotropic, infinite in extent, and unchanging, then any line of sight from Earth should eventually meet a star and the entire night sky should be bright. Since the night sky is obviously dark, this contradiction is known as Olbers’s paradox.

26.2 The Expanding Universe So, why is it dark at night? The universe is homogeneous and isotropic—it must not be infinite or unchanging. We have already found that galaxies are moving faster away from us the farther away they are: recession velocity = H0 x distance

26.2 The Expanding Universe So, how long did it take the galaxies to get there? time = distance / velocity = distance / (H0 x distance) = 1/H0 Using H0 = 70 km/s/Mpc, we find that time is about 14 billion years.

26.2 The Expanding Universe Note that Hubble’s law is the same no matter who is making the measurements. Figure 26-4. Hubble Expansion Hubble’s law is the same, regardless of who makes the measurements. The top numbers are the distances and recessional velocities as seen by an observer on the middle of five galaxies, galaxy 3. The bottom two sets of numbers are from the points of view of observers on galaxies 2 and 1, respectively. In all cases, Hubble’s law holds: The ratio of the observed recession velocity to the distance is the same.

26.2 The Expanding Universe If this expansion is extrapolated backward in time, all galaxies are seen to originate from a single point in an event called the Big Bang. So, where was the Big Bang? It was everywhere! No matter where in the universe we are, we will measure the same relation between recessional velocity and distance with the same Hubble constant.

26.2 The Expanding Universe This can be demonstrated in two dimensions. Imagine a balloon with coins stuck to it. As we blow up the balloon, the coins all move farther and farther apart. There is, on the surface of the balloon, no “center” of expansion. Figure 26-5. Receding Galaxies Coins taped to the surface of a spherical balloon recede from each other as the balloon inflates (left to right). Similarly, galaxies recede from each other as the universe expands. As the coins separate, the distance between any two of them increases, and the rate of increase of this distance is proportional to the distance between them.

26.2 The Expanding Universe The same analogy can be used to explain the cosmological redshift. Figure 26-6. Cosmological Redshift As the universe expands, photons of radiation are stretched in wavelength, giving rise to the cosmological redshift. In this case, as the baseline in the diagram stretches, the radiation shifts from the short-wavelength blue region of the spectrum to the longer wavelength red region. (Sec. 3.1)

26.2 The Expanding Universe These concepts are hard to comprehend, and not at all intuitive. A full description requires the very high-level mathematics of general relativity. However, there are aspects that can be understood using relatively simple Newtonian physics—we just need the full theory to tell us which ones!

26.3 The Fate of the Cosmos There are two possibilities for the universe in the far future: It could keep expanding forever. It could collapse. Assuming that the only relevant force is gravity, which way the universe goes depends on its density.

26.3 The Fate of the Cosmos If the density is low, the universe will expand forever. If it is high, the universe will ultimately collapse. Figure 26-8. Model Universes Distance between two galaxies as a function of time in each of the two basic universes discussed in the text: a low-density universe that expands forever and a high-density cosmos that collapses. The point where the two curves touch represents the present time.

26.3 The Fate of the Cosmos There is a critical density between collapse and expansion. At this density the universe still expands forever, but the expansion speed goes asymptotically to zero as time goes on. Given the present value of the Hubble constant, that critical density is approximately 9 x 1027 kg/m3 This is about five hydrogen atoms per cubic meter.

26.3 The Fate of the Cosmos If space is homogenous, there are three possibilities for its overall structure: Closed—this is the geometry that leads to ultimate collapse Flat—this corresponds to the critical density Open—expands forever

26.4 The Geometry of Space These three possibilities can be described by comparing the actual density of the Universe to the critical density. Astronomers refer to the actual density of the Universe as Ω, and to the critical density as Ω0. Then we can describe the three possibilities as Ω < Ω0 Open geometry Ω = Ω0 Flat geometry Ω > Ω0 Closed geometry

26.4 The Geometry of Space In a closed universe, you can travel in a straight line and end up back where you started (in the absence of time and budget constraints, of course!) Figure 26-10. Einstein’s Curve Ball In a closed universe, a beam of light launched in one direction might return someday from the opposite direction after circling the universe, just as motion in a “straight line” on Earth’s surface will eventually encircle the globe.

More Precisely 26-1: Curved Space The three possibilities for the overall geometry of space are illustrated here: The closed geometry is like the surface of a sphere; the flat one is flat; and the open geometry is like a saddle.

26.5 Will the Universe Expand Forever? The answer to this question lies in the actual density of the universe. Measurements of luminous matter suggest that the actual density is only a few percent of the critical density. But, we know there must be large amounts of dark matter.

26.5 Will the Universe Expand Forever? However, the best estimates for the amount of dark matter needed to bind galaxies in clusters, and to explain gravitational lensing, still only bring the observed density up to about 0.3 times the critical density, and it seems very unlikely that there could be enough dark matter to make the density critical.

26.5 Will the Universe Expand Forever? Type I supernovae can be used to measure the behavior of distant galaxies. If the expansion of the universe is decelerating, as it would be if gravity were the only force acting, the farthest galaxies had a more rapid recessional speed in the past, and will appear as though they were receding faster than Hubble’s law would predict.

26.5 Will the Universe Expand Forever? However, when we look at the data, we see that they correspond not to a decelerating universe, but to an accelerating one. This acceleration cannot be explained by current theories of the universe, although we do know it is not caused by either matter or radiation. Figure 26-11. Accelerating Universe (a) In a decelerating universe (purple and red curves), redshifts of distant objects are greater than would be predicted from Hubble’s law (black curve). The reverse is true for an accelerating universe. The data points show observations of some 50 supernovae that strongly suggest cosmic expansion is accelerating. (b) The bottom frames show three Type-I supernovae (marked by arrows) that exploded in distant galaxies when the universe was nearly half its current age. The top frames show the same areas prior to the explosions. (CfA; NASA)

26.5 Will the Universe Expand Forever? The repulsive effect of the dark energy increases as the universe expands. Figure 26.12 Dark Energy The expansion of the universe is opposed by the attractive force of gravity and sped up by the repulsion due to dark energy. As the universe expands, the gravitational force weakens, whereas the force due to dark energy increases. A few billion years ago, dark energy began to dominate, and the expansion of the cosmos has been accelerating ever since.

Discovery 26-1: Einstein and the Cosmological Constant The cosmological constant (vacuum energy) was originally introduced by Einstein to prevent general relativity from predicting that a static universe (then thought to be the case) would collapse. When the universe turned out to be expanding, Einstein removed the constant from his theory, calling it the biggest blunder of his career.

Discovery 26-1: Einstein and the Cosmological Constant Now, it seems as though something like a cosmological constant may be necessary to explain the accelerating universe—theoretical work is still at a very early stage, though!

26.6 Dark Energy and Cosmology What else supports the “dark energy” theory? In the very early life of the universe, the geometry must be flat. The assumption of a constant expansion rate predicts the universe to be younger than we observe.

26.6 Dark Energy and Cosmology This graph now includes the accelerating universe. Given what we now know, the age of the universe works out to be 13.7 billion years. Figure 26-15. Cosmic Age The age of a universe without dark energy (represented by all three lower curves colored red, purple, and blue) is always less than 1/H0 and decreases for larger values of the present-day density. The existence of a repulsive cosmological constant increases the age of the cosmos, as shown by the green curve that is drawn using the best available cosmic parameters, as described in the text.

26.6 Dark Energy and Cosmology This is consistent with other observations, particularly of the age of globular clusters, and yields the following timeline: 14 billion years ago: Big Bang 13 billion years ago: Quasars form 10 billion years ago: First stars in our galaxy form

26.7 Cosmic Microwave Background The cosmic microwave background was discovered fortuitously in 1964, as two researchers tried to get rid of the last bit of “noise” in their radio antenna. Instead, they found that the “noise” came from all directions and at all times, and was always the same. They were detecting photons left over from the Big Bang. Figure 26-16. Microwave Background Discoverers This “sugarscoop” antenna was built to communicate with Earth-orbiting satellites, but was used by Robert Wilson (right) and Arno Penzias to discover the 2.7-K cosmic background radiation. (Alcatel-Lucent)

26.7 Cosmic Microwave Background When these photons were created, it was only one second after the Big Bang, and they were very highly energetic. The expansion of the universe has redshifted their wavelengths so that now they are in the radio spectrum, with a blackbody curve corresponding to about 3 K. Figure 26-17. Cosmic Blackbody Curves Theoretically derived blackbody curves for the entire universe (a) 1 second after the Big Bang, (b) 100,000 years later, (c) 10 million years after that, and (d) today, approximately 14 billion years after the Big Bang.

26.7 Cosmic Microwave Background Since then, the cosmic background spectrum has been measured with great accuracy. Figure 26-18. Microwave Background Spectrum The intensity of the cosmic background radiation, as measured by the COBE satellite, agrees very well with theory. The curve is the best fit to the data, corresponding to a temperature of 2.725 K. Experimental errors in this remarkably accurate observation are smaller than the dots representing the data points.

26.7 Cosmic Microwave Background A map of the microwave sky shows a distinct pattern, due not to any property of the radiation itself, but to the Earth’s motion. Figure 26-19. Microwave Sky A COBE map of the entire sky reveals that the microwave background appears a little hotter in the direction of the constellation Leo and a little cooler in the opposite direction. (NASA)

Summary of Chapter 26 On scales larger than a few hundred megaparsecs, the universe is homogeneous and isotropic. The universe began about 14 million years ago, in a Big Bang. The future of the universe: It will either expand forever, or collapse. Density between expansion and collapse is critical density.

Summary of Chapter 26 (cont.) A high-density universe has a closed geometry; a critical universe is flat; and a low-density universe is open. Luminous mass and dark matter make up at most 30% of the critical density. Acceleration of the universe appears to be speeding up, due to some form of dark energy. The universe is about 14 billion years old. Cosmic microwave background is photons left over from Big Bang.