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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?
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.
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.
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.
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.
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.
- 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).
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.
- 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.
- 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.
- 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.
- Absorption lines from hydrogen in quasar spectra tells us that there is
a lot of material between us and the quasars.
- 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).
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 |
- 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?
- Why is the universe's expansion rate slowing down?
- Will it ever slow down completely? How can you find out?
- 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?
- 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!
- 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?
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.
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.
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.
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!
Back to
cosmic microwave background and early universe sections
last update: 06 April 1999
Nick Strobel --
Email:
strobel@lightspeed.net
(661) 395-4526
Bakersfield College
Physical Science Dept.
1801 Panorama Drive
Bakersfield, CA 93305-1219