Fate of the Universe
The Universe is currently expanding. One extremely important cosmological question
is whether this expansion will continue forever. As we shall see later, this is a
question that does not yet have a definitive answer. Ultimately, this will
hinge on how much mass is contained in the Universe (that is, its average density),
and of whether the
cosmological constant has a finite value. To simplify the discussion, we shall assume that the
cosmological constant is zero and then return to the consequences that are implied if this is
not so.
In this case of vanishing cosmological constant, if the density is below a
critical amount the Universe will expand forever. If it is above the critical
amount, the expansion will eventually reverse and the Universe will collapse on
itself, leading to what has been termed the big crunch. If it is exactly
equal to the critical amount, the expansion will slow, but will stop only after an
infinite amount of time. Thus, in this case the Universe will expand forever too.
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Value of the Critical Density
The value of the critical density for our Universe is a remarkably small number.
In mass and equivalent energy units,
D0
= 7.9 x 10-27
kg/m3
= 4.5
GeV/m3
This is an average density of only about 5 hydrogen atoms for every cubic meter
of space in the Universe. However, we can express the critical density in yet another set of
units that is also instructive.
D0
= 6.6 x 1011
solar masses/Mpc3
This is close (within a factor of 10) to the actual density of the Universe, since the
mass is close to that of a galaxy and the average spacings between galaxies are near
1 Mpc. This tells us that our Universe is not very far from the critical density.
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Is the Universe Open, Flat, or Closed?
The geometry of the Universe is
often expressed in terms of the density parameter, which is
defined to the the ratio of the actual density of the Universe to the critical density
that would just be required to cause the expansion to stop. This critical density is
also called
closure density. Its value is given in the adjacent right box.
In terms of the actual
density D and the critical density D0
Density Parameter = Ω0 = D/D0
Thus, if
the Universe is flat (contains just the amount of mass to close it) the density
parameter is exactly 1, if the Universe is open with negative curvature the density
parameter lies between 0 and 1, and if the Universe is closed with positive curvature the
density parameter is greater than 1. These three possible categories for the
large-scale geometry of the Universe are summarized in the
following table and in the top right figure
in terms of the density parameter Ω0 =
D/D0.
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Density and the Fate of the Universe
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| D/D0 |
Geometry |
Fate of the Universe
|
| < 1 |
Open |
Expand forever
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| >1 |
Closed |
Expansion, then contraction
|
| 0 |
Flat (Euclidean) |
Expansion stops only after
infinite time |
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These considerations assume that the cosmological constant is zero. As we shall discuss
further below, if the cosmological constant is not zero the fate of the Universe is more
complex. In that case,
the future behavior of the cosmos
depends not only on the density of matter and radiation, but also on the vacuum
energy density. The condition for a flat geometry also becomes more complex because it must
account for both the influence of matter and radiation, and the vacuum energy density, on the
curvature of the Universe.
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The Density Parameter
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| Source |
Value
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| Baryons (BB
nucleosynthesis) |
0.031
|
| Stars in Galaxies |
0.004
|
| Intergalactic Stars |
< 0.04
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| Rich Clusters |
0.01
|
| Dynamics (r < 15 Mpc) |
~ 0.05 - 0.2
|
| Dynamics (r > 50 Mpc) |
~ 0.05 - 1 |
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Source: P. J. E. Peebles, Principles of
Physical Cosmology
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The Observed Value of the Density Parameter
The density parameter determined from various methods is summarized in the
adjacent table. In this table, BB nucleosynthesis
refers to constraints coming from the synthesis of
the light elements in the big bang.
Although most of these methods (which we will not discuss in detail) yield values of the
density parameter far below the critical value of 1, we must remember that they
have likely not detected all matter in the Universe yet. A typical modern number for the
amount of mass identified in the Universe (both luminous and dark) gives perhaps 30-40 percent
of the closure density, but this number could well be revised by future discoveries.
The value of the density parameter
and thus the ultimate fate of the Universe remains one of the major
unsolved problems in modern cosmology.
