Chapter 26 Cosmology II Future and Issues Now that you have explored the beginnings of the universe and have an answer to the question ``where did we come from?'', let's address the other question, ``where are we going?'' This final section will cover the fate of the universe We observe that the universe is expanding and that gravity is slowing it down Which of them will win? The Future of the Universe Depends on Mass (Curvature of Space) The more mass there is the more gravity there is to slow down the expansion Is there enough gravity to halt the expansion and recollapse the universe or not? If there is enough matter (gravity) to recollapse the universe, the universe is ``closed'' In the examples of curved space above, a closed universe would be shaped like a four-dimensional sphere (finite, but unbounded) Space curves back on itself and time have a beginning and an end If there is not enough matter, the universe will keep expanding forever Such a universe is ``open'' In the examples of curved space, an open universe would be shaped like a four-dimensional saddle (infinite and unbounded) Space curves away from itself and time has no end GEOL 1401 1/11/2010 1
Instead of trying to add up all of the mass in the universe, a more reasonable thing to do is to find the density of a representative region of the universe The density = (mass in the region)/(volume of the region) If the region is truly representative, then the total mass of the universe = the density the total volume of the universe If the density is great enough, then the universe is closed If the density is low enough, then the universe is open In the popular astronomy magazines, you will probably see the mass density of the universe specified by the symbol `` '' It is the ratio of the current density to the ``critical density'' described in the next paragraph If < 1, the universe is open; if > 1, the universe is closed Critical Density The boundary density between the case where the universe has enough mass/volume to close universe and too little mass/volume to stop the expansion is called the critical density The critical density = 3H 2 G), where H is the Hubble constant for a given cosmological time Notice that the Hubble constant has appeared again! It measures the expansion rate, so it should be in the critical density relation The current critical density is approximately 106 10-29 g/cm3 This amounts to six hydrogen atoms per cubic meter on average overall A critical density universe has ``flat'' curvature The density parameter equals exactly 1 in a flat universe The Hubble ``constant'' is not really a constant it is different at different cosmological times The greater the value of the Hubble constant at a given cosmological time, the faster the universe is expanding at that time Gravity slows the expansion of the universe, so the early universe was expanding faster than it is now That means that the critical density was greater at earlier times It changes by the same factor that the actual density of the universe changes throughout the expansion So if the universe starts out with a density greater than the critical density, then its density will always be greater than critical density If the universe starts out with a density less than the critical density, then its density will always be less than the critical density Is The Universe Open or Closed? GEOL 1401 1/11/2010 2
The curvature of the universe is determined by the density of the universe You can do a cosmic inventory of all of the mass from ordinary matter in a representative region of the universe to see if the region's density is above the critical density Such an inventory gives 10 to 20 times too little mass to close the universe The primordial deuterium abundance provides a sensitive test of the density of ordinary matter in the early universe Again, you get 5 to 15 times too little mass to close the universe However, these measurements do not take into account all of the dark matter known to exist Dark matter is all of the extra material that does not produce any light, but whose presence is detected by its significant gravitational effects Dark Matter There may be about 90 times more dark matter mass than visible matter Some of the dark matter is regular sort of matter (atoms) that is too faint for us to detect such as dead burned out stars, planets, brown dwarfs, etc The rest of the dark matter is made of material that is not made of atoms or their constituent parts This strange material has a total mass almost six times more than the total mass of the ordinary matter Some evidence for the presence of dark matter has already been presented in the previous chapters The list below summarizes the evidence for dark matter's existence Orbital speeds of stars in galaxies Flat rotation curves of spirals even though the amount of the light-producing matter falls off as the distance from the galaxy center increases Remember the enclosed mass = (orbital speed) 2 (orbit size)/g Below is the rotation curve for our Milky Way Galaxy (a typical spiral galaxy) GEOL 1401 1/11/2010 3
Also, the orbital speeds of stars in elliptical galaxies are too high to be explained by the gravitational force of just the luminous matter in the galaxies The extra gravitational force is supplied by the dark matter in the ellipticals Faint gas shells around ellipticals Ellipticals have faint gas shells that need massive "dark" haloes to contain them The gas particles are moving too quickly (they are too hot) for the gravity of the visible matter to hang onto it However, the number of ellipticals with these faint gas shells is too large to be only a temporary feature of ellipticals The dark haloes must extend out to 300,000 light years around each galaxy The extent of this dark matter pushes up to around 02 If the haloes are larger than originally thought, could approach 1 Motion of galaxies in a cluster Galaxy cluster members are moving too fast to be gravitationally bound unless there is unseen mass The reasonable assumption is that we do not live at a special time, so the galaxies in the cluster must have always been close to each other The large velocities of the galaxies in the clusters are produced by more gravity force than can be explained with the gravity of the visible matter in the galaxies Hot gas in clusters The existence of HOT (ie, fast moving) gas in galaxy clusters To keep the gas bound to the cluster, there needs to be extra unseen mass Quasar spectra Absorption lines from hydrogen in quasar spectra tell us that there is a lot of material between us and the quasars GEOL 1401 1/11/2010 4
Gravitational Lensing Gravitational lensing of the light from distant galaxies and quasars by closer galaxies or galaxy clusters enables us to calculate the amount of mass in the closer galaxy or galaxy cluster from the amount of bending of the light The derived mass is greater than the amount of mass in the visible matter Dark Matter separation from ordinary matter The collision of the galaxy cluster 1E 0657-56, called the "bullet cluster", with another galaxy cluster has produced a clear separation of the ordinary matter from the dark matter The ordinary matter of one cluster is slowed by a drag force as it interacts with the gas (ordinary matter) of the other cluster The dark matter is not slowed by the impact because it responds only to gravity and is not affected by gas pressure In the picture below, the ordinary matter is colored pink---it is hot gas imaged by the Chandra X-ray Observatory The blue areas are where most of the mass in the clusters is found (the dark matter) The dark matter locations were determined by gravitational lensing of light from background galaxies Select the Chandra link to view animations of how the separation happened Current tallies of the total mass of the universe (visible and dark matter) indicate that there is only 26% of the matter needed to halt the expansion---we live in an open universe Astronomers and physicists are exploring the possibility that perhaps there is an additional form of energy not associated with ordinary or dark matter, called "dark energy that would greatly affect the fate of the universe This is discussed in the last section of this chapter Deriving the Geometry of the Universe from the Background Radiation GEOL 1401 1/11/2010 5
An independent way to measure the overall geometry of the universe is to look at the fluctuations in the cosmic microwave background radiation If the universe is open (saddle-shaped), then lines starting out parallel will diverge (bend) away from each other This will make distant objects look smaller than they would otherwise, so the ripples in the microwave background will appear largest on the half-degree scale If the universe is flat, then lines starting out parallel will remain parallel The ripples in the microwave background will appear largest on the 1-degree scale If the universe is closed, the lines starting out parallel will eventually converge toward each other and meet This focusing effect will make distant objects look larger than they would otherwise, so the ripples in the microwave background will appear largest on scales larger than 1-degree Select the image below to go to the WMAP webpage from which the image came The resolution of the COBE satellite was about 7 degrees---not good enough to definitively measure the angular sizes of the fluctuations After COBE, higher-resolution instruments were put up in high-altitude balloons and high mountains to observe the ripples in small patches of the sky Those experiments indicated a flat geometry for the universe Cosmologists using the high resolution of the WMAP satellite to look at the distribution of sizes of the ripples confirmed that conclusion using its all-sky map of microwave background at a resolution over 30 times better than COBE WMAP also gave a much improved measurement of the ripples The distribution of the ripples peaks at the one-degree scale---the universe is flat This result from the WMAP satellite and the too meager amount of matter in the universe to make the universe geometry flat is forcing astronomers to conclude that there is another form of energy that makes up 74% of the universe (called "dark energy" for lack of anything better) The "dark energy" is probably the "cosmological constant" discussed in the last section of this chapter Issues with the Big Bang Model GEOL 1401 1/11/2010 6
Flatness Problem There are a couple of problems with the standard Big Bang model The first is called the flatness problem---why is the universe density so nearly at the critical density or put another way, why is the universe so flat? Currently, the universe is so well-balanced between the positively-curved closed universe and the negatively-curved open universe that astronomers have a hard time figuring out which model to choose Of all the possibilities from very positively-curved (very high density) to very negatively-curved (very low density), the current nearly flat condition is definitely a special case The balance would need to have been even finer nearer the time of the Big Bang because any deviation from perfect balance gets magnified over time For example, if the universe density was slightly greater than the critical density a billion years after the Big Bang, the universe would have recollapsed by now Consider the analogy of the difficulty of shooting an arrow at a small target from a distance away If your angle of shooting is a little off, the arrow misses the target The permitted range of deviation from the true direction gets narrower and narrower as you move farther and farther away from the target The earlier in time the universe's curvature became fixed, the more finely tuned the density must have been to make the universe's current density be so near the critical density If the curvature of the universe was just a few percent off from perfect flatness within a few seconds after the Big Bang, the universe would have either recollapsed before fusion ever began or the universe would expanded so much that it would seem to be devoid of matter It appears that the density/curvature was very finely tuned Horizon Problem The second problem with the standard Big Bang model is the horizon problem---why does the universe, particularly the microwave background, look the same in all directions? The only way for two regions to have the same conditions (eg, temperature), is that they are close enough to each other for information to be exchanged between them so that they can equilibrate to a common state The fastest speed that information can travel is the speed of light If two regions are far enough apart that light has not had enough time to travel between the regions, the regions are isolated from each other The regions are said to be beyond their horizons because the regions cannot be in contact with each other (recall the term event horizon in the discussion about black holes) The photons from the microwave background have been travelling nearly the age of the universe to reach us right now Those photons have certainly not had the time to travel across the entire universe to the regions in the opposite direction from which they came Yet when astronomers look in the opposite directions, they see that the microwave background looks the same to very high precision How can the regions be so precisely the same if they are beyond each other's horizons? Running the expansion backward, astronomers find that regions even a degree apart in angular separation on our sky would have been beyond each other's horizons at the time the microwave background was produced Inflation On theoretical grounds, astronomers think that the very early universe experienced a time of ultra-fast expansion (called inflation) The inflation probably took place from about 10-38 to 10-36 seconds after the Big Bang, but astronomers are not sure of the cause of inflation so they cannot GEOL 1401 1/11/2010 7
pinpoint the time it would have occurred The size of the fluctuations in the cosmic microwave background indicates that the inflation could not have occurred before 10-38 seconds after the Big Bang The leading theory for the cause of the inflation says that it occurred when there was a break in the fundamental forces of nature Before the time of 10-38 seconds after the Big Bang, the fundamental forces of the strong nuclear force, the weak nuclear force, and electromagnetic force behaved in the same way under the extreme temperatures They were part of the same fundamental unified force Theories that describe the conditions when the forces were unified are called Grand Unified Theories (GUTs for short) At about 10-38 seconds after the Big Bang, the universe had cooled down to "only" 1029 K and the strong nuclear force broke away from the weak nuclear and electromagnetic forces This breaking apart of the forces from each other somehow produced the huge expansion that expanded the universe by about 1050 times in about 10-36 seconds History of the universe from the Big Bang to the Present Day The inflation theory predicts that the ultra-fast inflation would have expanded away any largescale curvature of the part of the universe we can detect It is analogous to taking a small globe and expanding it to the size of the Earth The globe is still curved but the local piece you would see would appear to be fairly flat The small universe inflated by a large amount and the part of the universe you can observe appears to be nearly flat That solves the flatness problem GEOL 1401 1/11/2010 8
The horizon problem is solved by inflation because regions that appear to be isolated from each other were in contact with each other before the inflation period They came into equilibrium before inflation expanded them far away from each other Another bonus is that the GUTs that predict inflation also predict an asymmetry between matter and antimatter, so that there should be an excess of matter over antimatter The inflation theory might also explain where the ripples in the microwave background (the "galaxy seeds") come from Recall in an earlier section about the very early universe that matterantimatter can change to energy and energy can change back to matter-antimatter The laws of physics that deal with the very small scales of atoms, sub-atomic particles, etc (quantum mechanics) predict that the matter-energy fluctuations should be going on even today at every point in space It turns out that these quantum fluctuations can occur if they happen quickly enough to not be noticed (the greater the energy-matter fluctuation, the quicker the fluctuation must occur) Therefore, even in perfectly empty space (complete vacuum), there is a seething froth of fluctuations at very tiny scales, a vacuum energy---matter-antimatter virtual particles spontaneously appearing and then annihilating each other too quickly for us to detect GEOL 1401 1/11/2010 9
Although virtual particles-quantum foam might seem a bit too fanciful (to put it kindly), these virtual particles do produce measurable effects such as: In an atom, the appearance of electron-positron virtual particles will alter the orbit of the real electron orbiting the nucleus altering the energy levels which can be measured with very sensitive, precise equipment The measured energy levels agree with those predicted by quantum if virtual particles are taken into account Extra forces generated between close metal plates (the "Casimir Effect") can be explained by the presence of more virtual particles on either side of the plates than in the gap between the plates Collisions of real particles and real antiparticles in high-energy particle accelerators can supply energy to the vacuum and cause other particle-antiparticles to appear Now back to inflation The quantum fluctuations in the very early universe could have been the galaxy seeds, but they would have been much too small to be the ripples we see in the cosmic microwave background Before inflation that is! The super-rapid growth of the universe during inflation would have stretched the fluctuations to much larger sizes---large enough to create the ripples in the microwave background that eventually became enhanced to form galaxies under the action of gravity over billions of years Although the current versions of inflation theory cannot answer all of the questions about the large-scale structures of our universe, they do predict a particular distribution of the ripple sizes in the microwave background that is consistent with the results from the high-altitude balloon experiments and WMAP The distribution of the ripples peaks at an angular size of one degree on the sky and the temperature varies by about 1 part in 100,000 as predicted by inflation As astronomers continue to gather data from WMAP and the future PLANCK spacecraft, they will be looking at how the microwave background photons scattered off the electrons just before the universe became transparent Scattering causes light to become preferentially oriented in a particular way (it is "polarized") The simplest version of inflation predicts a particular polarization of the microwave background that appears to be seen in the WMAP data WMAP and PLANCK will look for the imprint of gravitational waves predicted by the inflation theory The Cosmological Constant GEOL 1401 1/11/2010 10
Albert Einstein completed his theory of General Relativity in 1915 When he applied his theory to the spacetime of the universe, he found that gravity would not permit the universe to be static Over a decade before Hubble's discovery of an expanding universe, Einstein made the reasonable assumption that the universe is static and unchanging (the perfect cosmological principle) He introduced a term called the cosmological constant that would act as a repulsive form of gravity to balance the attractive nature of gravity The cosmological constant is an exotic form of energy filling empty space, the vacuum energy discussed above The vacuum energy creates a repulsive gravitational force that does not depend on position or time; it truly is a constant When Einstein learned of Hubble's discovery, he realized that he should have had more faith in his original General Relativity He discarded the cosmological constant as the "biggest blunder of his life" Recent observations are indicating that the cosmological constant should be brought back Astronomers are finding that even when they include the maximum amount of dark matter allowed by the observations, there is not enough matter (luminous or dark) to flatten the universe---the universe is open with negative curvature if the cosmological constant is zero The inflation theory predicts that the universe should be flat to very high precision An extra energy called dark energy is needed to make the universe curvature flat overall beyond what ordinary and dark matter can do This dark energy is probably the cosmological constant (vacuum energy) described above Recent observations of the cosmic microwave background show that the combined efforts of matter and dark energy flatten space as much as that predicted by inflation theory One major stumbling block in the theory of the cosmological constant is that quantum theory predicts that the total vacuum energy should be on the order of 10120 times larger than what is observed The cosmological constant predicted from quantum theory would cause the universe to expand so fast that you would not be able to see your hand in front of your face because the light would not be able to reach your eyes! In reality we can see to billions of light years Physicists are trying to figure out why there is such a big discrepancy between the quantum theory's prediction and observation Some cosmologists are exploring the idea of a dark energy that varies with space and time called "quintessence" Stay tuned for developments! Another set of observations of very distant ("high-z") Type Ia supernovae show that the expansion rate is slower than expected from a flat universe Type Ia supernovae are very luminous and can be used as standard candles to measure very large distances because they form from the collapse of a stellar core of a particular mass (14 solar masses) By measuring very large distances, astronomers can determine the geometry of the universe The supernovae are fainter than expected After exploring ordinary possibilities like intergalactic dust, gravitational lensing effects, and metallicity effects, astronomers are forced to conclude that either the universe has negative curvature (is open) or that the supernovae are farther away than the Hubble Law says they are their redshifts are "too small" because the universe expanded more slowly in the past than expected What is surprising about the supernova observations is that they may indicate that the expansion is accelerating! GEOL 1401 1/11/2010 11
Accelerating expansion is impossible without a repulsive cosmological constant to overcome the slowing down effect of gravity An accelerating universe will increase the derived age of the universe because the expansion rate long ago was slower than the expansion rate is now The galaxies needed more time to get to their large distances than the original decelerating universe model said Long ago gravity was the dominant force affecting the universe's expansion since everything was closer together As the universe expanded the effect of gravity got diluted Eventually, the strength of gravity dropped below the amount of the dark energy Recent observations of how the expansion rate has changed over the history of the universe show that the dark energy began to dominate over gravity about 4 billion to 6 billion years ago but its presence being felt up to about 9 billion years ago The far future of the universe depends on the form that dark energy takes If the dark energy is the cosmological constant, then the expansion of the universe will continue long after all of the stars have died out many trillions of years in the future If the dark energy is one of the possible forms of "quintessence", the acceleration rate increases and the galaxies, stars, even atoms are torn apart in a big rip on a time scale before the entire universe of stars die out (but after our Sun die) Other forms of the dark energy could cause the universe to re-collapse after its current period of acceleration Detailed studies of the microwave background and further observations of supernovae with better detectors and new larger space telescopes in the future will tell us if the dark energy is a cosmological constant or a quintessence form Results from the WMAP mission lean toward the cosmological constant form, but it might take the PLANCK mission to settle the matter However, we have learned enough from the past few years of surprising observations to say that Einstein's greatest blunder was saying that he made a blunder! GEOL 1401 1/11/2010 12
Review Questions and Vocabulary Vocabulary o Closed Universe o Critical Density o Dark Matter o Flat Universe o Open Universe o Cosmological Constant o Dark Energy o Inflation Review Questions 1 What is the overall curvature of space in a closed or open or flat universe? How does the expansion rate compare to the amount of gravity deceleration in each of these cases? 2 Why is the universe's expansion rate slowing down? 3 Will it ever slow down completely? How can you find out? 4 What type of universe has a critical density? What would happen to the expansion if the current density < critical density? How about the case for the current density > critical density? 5 Would a universe starting out with a density > critical density ever expand enough so its density dropped below critical density? Explain why or why not! 6 What is all the fuss about dark matter? If it is not putting out any light for us to see, how is it known to exist? What are some examples of observations indicating its presence? 7 How can you use the cosmic microwave background (something from the far past) to determine the fate of the universe (something in the far future)? 8 What is the "flatness" problem in the standard Big Bang theory? How is it a finetuning problem? 9 What is the "horizon" problem in the standard Big Bang theory? 10 What is the inflation extension of the Big Bang theory and when is thought to have occurred in the universe's history? 11 How does the inflation extension of the Big Bang theory explain the "flatness" and "horizon" problems that are part of the standard Big Bang theory? 12 How do we know that quantum fluctuations - virtual particles exist? 13 What is the "cosmological constant" and why did Einstein invent it? Why did Einstein say that was a mistake? Why do cosmologists now say it was not a mistake? 14 How does dark energy affect the expansion of the universe? GEOL 1401 1/11/2010 13
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