As evidence has accumulated in support of the Big Bang theory, the theory has come under
increasingly close scrutiny, as are all
scientific theories.
Questions have been raised for which the theory provides puzzling or even contradictory answers. The questions are
posed in the form of problems: the flatness problem, the horizon problem, and the monopole
problem. Solving these problems requires an extension of the Big Bang called
inflation: a theory that the universe began by expanding exponentially in size.
Flatness Problem
Observations in astronomy, by 1981, revealed that the universe is almost flat, where flat
means that parallel lines in space are always parallel. Surprisingly "almost flat" creates
a difficulty for the Big Bang theory. Today's flatness is measured by the parameter
Ω_{0}
(omega naught), and an almost flat universe today means that Ω
_{0} has a value near 1, maybe as
small as 0.5 or maybe as large as 1.5.
Because the universe is expanding, a natural question to ask is "has the universe always
been nearly flat, or has it become flat by expanding"? Answering the question is not difficult,
using the Big Bang theory, but the theory's answer is a surprise and is unsatisfactory.
In the demo, choose a flatness value for today (Ω
_{0}), but don't choose 1.
Then click on each of the three Earlier Time Era options and their corresponding UniverseScale values
in turn. Notice what happens to earlier flatness values, as the time of the Big Bang is approached.
(The CDF player may take a couple of minutes to load.)
You should notice that at the "Earliest Possible Time," the universe is flatter than at
any later time, as measured by the closeness of earlier values of Ω to 1. But is this sensible?
Wouldn't you expect the universe to become flatter as it expands, in the way that a large ball
has a flatter surface than a small ball's? Aside from the ball analogy, is it likely that
the universe is almost flat to so many decimal places at an earlier time, but isn't exactly flat? Cosmologists
have reasoned that it is unlikely that the universe becomes less flat as it ages. What
is more likely is that the universe is exactly flat (Ω=1), but this is not what the Big Bang
theory demonstrates. This is called the
flatness problem.
Horizon Problem
Electrons, protons, and photons (particles of light) form a "soup" of particles vigorously colliding
with each other above 3,700 K. As the universe cools down to 3,000 K, electrons combine with protons
to form hydrogen atoms, and when that happens, 380,000 years after the Big Bang, light no longer scatters and is free to stream to
today's observers as
Cosmic Microwave Background (CMB) radiation.
Observation of the CMB gives valuable data about the time of light's last scattering.
For example, the CMB is observed to be uniform over the entire sky, implying that the temperature
of the universe today (2.7 K) is the same everywhere, and was the same (3,000 K) everywhere
at the time of last scattering. But is it reasonable that the temperature should be virtually the
same over the vast distances of the entire universe? Today the universe is so large that light has
traveled a distance of 45 billion light years since the Big Bang (today's horizon distance), so astronomical objects farther
than this (beyond the horizon) cannot be observed. At light's last scattering this distance was only 40 million light years
because of the smaller size of the universe. But, according to the Big Bang theory, uniformity
could exist at the last scattering time only over a distance of 1 million light years (the horizon distance, 380,000 years post Big Bang).
So at the time of light's last scattering, uniformity over a distance of 40 million light years was impossible.
Therefore, according to the Big Bang theory, temperatures at two points separated by distances greater than 1 million light
years (larger than the horizon distance) should not be the same. This is called the
horizon problem, and it is illustrated by
the demo below.
Monopole Problem
Both the flatness and horizon problems are revealed in the context of the standard Big Bang theory
as shortcomings of that theory. The monopole problem, however, is not part of the Big Bang theory
at all. It is a problem that arises when cosmologists attempt to construct a theory that goes
beyond the Big Bang to extremely early moments in the universe. The monopole problem can be
understood by anyone who has ever played with a bar magnet with north and south poles
stamped on the magnet. All magnets have north and south poles (they are alternated multiple
times on refrigerator magnets), and these opposite poles attract. But in the ambitious
early universe theories that aspire to go beyond the Big Bang by unifying electricity and magnetism with
nuclear forces (called
Grand Unified
models), the magnets have only one pole (a monopole), inconsistent with what's found in nature.
Inflation Theory: Problems Solved
Tackling these problems is made easier by imagining a solution to the monopole problem first,
and the only solution is to eliminate the monopoles because they are not found in nature.
Elimination, however, can also be accomplished by expanding, i.e. inflating, the universe
to such a large size that the number of monopoles to be found in any given volume is
essentially zero. Problem solved, apparently. But without mathematical expression of the
inflation idea, this solution is just a daydream.
We'll express inflation in math terms to solve the horizon problem. Consider a time (the Grand Unified Theory or GUT era)
10
^{−34} seconds after the Big Bang, when the universe size (scale factor) was a tiny 2×10
^{−27} times
its current size (=1). At that time, today's 45 billion light year horizon distance was reduced to 0.9 meters. But
the horizon distance at 10
^{−34} seconds is only 6×10
^{−26} meters,
the horizon problem once again: 0.9 meters >> 6×10
^{−26} meters.
What's needed is for a horizon distance today, extrapolated back to a past time, to be smaller than the
horizon distance at that time. Inflation models create the appropriate conditions by proposing that
our universe began at the incomprehensibly small size of 3.3×10
^{−44} meters
at 10
^{−36} seconds, then it undergoes exponential growth (inflation) until 10
^{−34} seconds
to a size of 0.9 meters. At 10
^{−36} seconds, however, the horizon size
is 6×10
^{−28} meters. We've finally reached the condition that
the horizon distance is larger than our current horizon, extrapolated back in time:
6×10
^{−28} meters >> 3.3×10
^{−44} meters.
Therefore, the incredibly tiny universe from which our universe has grown has the same temperature everywhere,
explaining why the temperature in our present universe is a uniform 2.7 K everywhere.
Inflation also solves the flatness problem by exponentially growing the initial
tiny universe out of any curvature, in the same way that the surface of a sphere becomes
flatter as it becomes larger. Even though the inflated region has a uniform temperature, there are
very small fluctuations from uniformity that also grow exponentially and are eventually
detectable as
fluctuations
in the Cosmic Background Radiation.