Astronomy 162: Professor Barbara Ryden
Wednesday, March 12
THE VERY EARLY UNIVERSE
``Though a good deal is too strange to be
believed, nothing is too strange to have happened.''
- Thomas Hardy
Key Concepts
- Horizon problem: Why is the universe so
smooth on large scales?
- Flatness problem: Why is the density so
close to the critical density?
- These problems are solved if the early universe underwent
a period of inflation.
(1) Horizon problem: Why is the universe so smooth
on large scales?
The temperature of the Cosmic Microwave Background (CMB) is
very nearly isotropic. That is, when you look at different
patches of the CMB, their temperatures are the same to
within 1 part in 10,000. This implies that when the
universe became transparent (about 300,000 years after
the Big Bang), it was very nearly homogeneous. The
homogeneity, or smoothness, of the universe is referred
to by cosmologists as the horizon problem.
So why is the homogeneity of the universe such a problem?
And why is it called a ``horizon'' problem? What does the
cosmic particle horizon got to do with it? Well, remember
that when we look at the Cosmic Microwave Background, we
are actually looking at the surface of the ionized opaque
``fog'' that filled the early universe. Because the universe
became transparent early in its history, long before the
present day, the distance to the opaque ``fog bank'' is
nearly equal to the our cosmic particle horizon distance.
(Our horizon distance is roughly 14 billion light-years;
the distance to the opaque ``fog'' is 99 percent of that value.)
Consider two antipodal points on the sky, as far apart
as they can be on the celestial sphere. Let's call them
point A and point B.
- CMB photons from point A have traveled a distance
equal to 0.99 times the horizon distance in order to reach us.
- CMB photons from point B have also traveled a distance
equal to 0.99 times the horizon distance in order to reach us.
- Since A and B are in opposite directions as seen by us,
the distance from A to B is 0.99 + 0.99 = 1.98 times the
horizon distance.
What does this mean? Points A and B are separated by a distance
larger than the horizon distance. Hence, they are outside
each other's cosmic particle horizon, and are utterly unaware
of each other's existence. Despite their lack of communication,
they have the same temperature to better than one part in 10,000.
Is their extreme similarity in temperature just a coincidence?
Or did something happen in the early universe that permitted
points A and B to reach the same temperature?
(2) Flatness problem: Why is the density so close to the
critical density?
The density of the universe divided by the critical density
is a dimensionless number that is usually called the
density parameter, and is symbolized by
the Greek letter Omega. At the present moment, the density
parameter is very nearly equal to one, and thus the universe
is very nearly flat. The current best limits on Omega tell us
that
0.9 < Omega < 1.1
That is, the density of the universe is within 10 percent of
the critical density. Why should this be? There's no law of
physics that forbids the density to be a million times the
critical density, or one-millionth the critical density.
The coincidence between the actual density and the critical
density looks even fishier when you consider that any deviations
of the density and the critical density tend to grow with
time while the universe is dominated by light or by matter.
Today,
0.9 < Omega < 1.1
At t = 2500 years, when the universe became dominated by matter,
0.9999 < Omega < 1.0001
At t = 10^{-43} seconds, the earliest time that our
knowledge of physics permits us to contemplate,
0.9999999999999999999999999999999999999999999999999999999999999999 <
Omega <
1.0000000000000000000000000000000000000000000000000000000000000001
In other words, in order to be relatively flat today, the universe
had to be fanatically flat during its earliest stages. Why?
Was it just coincidence, or did something happen in the early
universe that flattened it out?
Before the year 1980, cosmologists were baffled by the horizon
problem and the flatness problem. They shrugged their shoulders
and said, ``The universe is fairly homogeneous and flat today because
it started out extremely homogeneous and flat. We don't know
why it was homogeneous and flat, it just was.''
In 1980, a cosmologist named Alan Guth proposed that the universe
became homogeneous and flat because it underwent a very early
period of inflation.
(3) These problems are solved if the early universe underwent
a period of inflation.
Inflation (at least in a cosmological context) can be defined
as a brief period of highly accelerated expansion, early in
the history of the universe. [According to current models of
particle physics, it's likely that inflation began at
t = 10^{-36} seconds after the Big Bang, and lasted
for a time t = 10^{-34} seconds. During this extremely
brief interval, inflation caused expansion by a factor of
10^{50} or so.
The idea of inflation (expansion by a factor of 100 trillion
trillion trillion trillion during a time of only 100 trillionths
of a trillionth of a trillionth of a second) is mind-bending.
Nevertheless, inflation provides a welcome solution to the
horizon problem and the flatness problem.
How does rapid inflation during the early universe solve the
horizon problem? To illustrate, consider our observable universe
(that is, the entire chunk of the universe that is bounded
by the opaque ionized ``fog''). The current radius of the
observable universe is 14 billion light years. At the
end of inflation, the radius of the observable universe
was a mere 3 x 10^{-9} light-seconds (about a yard).
Think of it! Everything that we can see -- including all the
mass of 100 billion galaxies -- squeezed into a sphere that
you could span with your arms. But, as Al Jolson once said,
you ain't heard nothing yet, folks. Because inflation caused
expansion by a factor of 10^{50} or so, before inflation
pumped up the observable universe, it was a mere 3 x 10^{-59}
light-seconds across. Note that at the start of inflation,
the horizon size was 10^{-36} light-seconds, far
larger than the minuscule patch that was fated to grow
into the currently observable universe. Thus, point A
and point B (and every other point within our observable
universe) had plenty of time, before inflation, to come
to the same temperature.
How does rapid inflation during the early universe solve
the flatness problem? To illustrate, suppose that the
early universe, before inflation, had positive curvature.
During inflation, all the distances in the universe increased
by a factor of 10^{50}. This meant that the radius
of the universe increased as well. If, for instance, the radius
of the universe was only one nanometer before inflation
(one billionth of a meter), after inflation, it would be
10 trillion trillion trillion light-years. Just as inflating
a balloon to larger and larger radii makes a small patch of
it look flatter and flatter, so inflating the universe makes
the small patch we call the ``observable universe'' look
flatter and flatter.
If you've been paying attention, you have noted that the
observable universe, during inflation, increased its radius
by r = 3 x 10^{-9} light-seconds during a time span
of only t = 10^{-34} seconds. To do this, the observable
universe would have to expand at a rate far, far faster than
the speed of light. ``Gasp!'' you may have said to yourself,
``Doesn't that violate the principles of relativity?'' Actually,
there's no need to panic. Objects moving through
space can't move faster than light with respect to each other.
However, when space itself expands, as happens in our Big Bang
universe, there's no restriction on its speed.
Prof. Barbara Ryden
(ryden@astronomy.ohio-state.edu)
Updated: 2003 Mar 10
Copyright © 2003, Barbara Ryden