Fate of the Universe

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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?

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 has 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.

curvature and possible fates of the universe

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 ``W''. It is the ratio of the current density to the ``critical density'' described in the next paragraph. If W < 1, the universe is open; if W > 1, the universe is closed.

measuring the density of our neighborhood to determine the fate of the universe

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 = 3H2/(8pG), where H is the Hubble parameter for our cosmological time. Notice that the Hubble parameter has appeared again! It measures the expansion rate, so it should be in the critical density relation. The current critical density is approximately 1.06 × 10-29 g/cm3. This amounts to six hydrogen atoms per cubic meter on average overall.

A critical density universe has ``flat'' curvature. The W density parameter equals exactly 1 in a flat universe. The parameter called the Hubble parameter is different at different cosmological times. 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?

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. This could be enough to make the universe's mass density = critical density. Some evidence for the presence of dark matter has already been presented in the previous chapter. The list below summarizes the evidence for dark matter's existence.

Orbital speeds of stars in galaxies

  1. 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).

    the Milky Way's rotation curve

    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.

    velocity dispersion of elliptical galaxies

    Faint gas shells around ellipticals

  2. 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 W up to around 0.2. If the haloes are larger than originally thought, W could approach 1.

    Motion of galaxies in a cluster

  3. 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

  4. The existence of HOT (i.e., fast moving) gas in galaxy clusters. To keep the gas bound to the cluster, there needs to be extra unseen mass.

    Quasar spectra

  5. Absorption lines from hydrogen in quasar spectra tells us that there is a lot of material between us and the quasars.

    Gravitational Lensing

  6. 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.

Current tallies of the total mass of the universe (visible and dark matter) indicate that there is too little matter 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 matter that would greatly affect the fate of the universe. This is discussed in the last section of this chapter.

A good book on the history of dark matter is The Dark Matter: Contemporary Science's Quest for the Mass Hidden in Our Universe by Wallace and Karen Tucker (New York: Morrow, 1988).

Deriving the Geometry of the Universe from the Background Radiation

An independent way to measure the overall geometry of the universe is to determine the largest angular size of the fluctuations in the cosmic microwave background radiation. If the universe is open, then the fluctuations are largest on the half-degree scale. If the universe is flat, then the fluctuations are largest on the degree scale and if the universe is closed, the fluctuations will be largest on even larger scales. The resolution of the instruments on the COBE satellite were not good enough to definitively measure the angular sizes of the fluctuations. A follow-up to the COBE mission called the Microwave Anisotropy Probe (MAP) will have the resolution to determine the curvature of the universe to within 5%. To find out more about how MAP will do this, go to their geometry page.

Vocabulary

closed universe critical density dark matter
flat universe inflation open universe

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?

Embellishments on the Big Bang

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.

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 (e.g., 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 took place at about 10-35 seconds after the Big Bang. Before that time, 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 10-35 seconds after the Big Bang, the universe had cooled down to ``only'' 1027 K and the strong nuclear force broke away from the weak nuclear and electromagnetic forces. This breaking apart of the forces from each other, produced the huge expansion that expanded the universe by about 1050 times in about 10-32 seconds.

super-rapid expansion removes the curvature

The inflation theory predicts that the ultra-fast inflation would have expanded away any large-scale 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. 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 Cosmological Constant

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, Einsten 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, a vacuum energy. 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. The extra vacuum energy can bend space as matter does. Perhaps the combined efforts of matter and vacuum energy could flatten space as much as that predicted by inflation theory.

Another set of observations of very distant Type I supernovae show that the expansion rate is slower than expected from a flat universe. Type I supernovae are very luminous and can be used as standard candles to measure very large distances and 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! Accelerating expansion is impossible without a repulsive cosmological constant to overcome the slowing down effect of gravity. Higher resolution observations of the microwave background by the MAP mission and further observations of supernovae with better detectors and new larger space telescopes in the future should tell us if Einstein's greatest blunder was saying that he made a blunder!

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last update: 06 April 1999


Nick Strobel -- Email: strobel@lightspeed.net

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Bakersfield College
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