Physicists define the boundaries of physics by trying
to describe them theoretically and then testing that description against
observation. Our observed expanding Universe is very well described
by flat space, with critical density supplied mainly by dark matter
and a cosmological constant, that should expand forever.
When the scale factor a(t) was very small, radiation
energy density was much larger than the matter and vacuum energy densities.
The temperature gets smaller as the scale factor rises:
The experimental understanding of particle physics
starts to poop out after energies above the electroweak unification
scale, around 1TeV. At a very small scale factor, or a very high temperature,
Grand Unified Theories, supersymmetry, and string theory have to be
taken into account in the cosmological modeling.
This exploration is guided by three outstanding problems
with the Big Bang cosmological model:
1. The flatness problem
2. The horizon problem
3. The magnetic monopole problem
Flatness problem
The Einstein equation predicts that any deviation
from flatness in an expanding Universe filled with matter or radiation
tends to grow larger as the Universe expands. The ratio of the matter
density to the curvature term in the Einstein equation
shows that tiny deviation from flatness at a much earlier time would
grow linearly with scale factor as the Universe grows and come to dominate
the evolution of the spacetime. This is consistent with the fact that
matter attracts matter through the gravitational force. Small lumps
are going to get bigger when gravity does its thing.
If the deviations from flatness are observed to be
very small today, then extrapolating back to when the Universe was much
smaller, the deviations from flatness must have been immeasurably small.
So why did the Big Bang start off with the deviations
from flat spatial geometry being immeasurably small? This is called
the flatness problem of Big Bang cosmology.
Horizon problem
The cosmic microwave background is the cooled remains
of the radiation from the radiationdominated phase of the Big Bang.
Observations of the cosmic microwave background show that it is highly
isotropic thermal radiation. The temperature
of this thermal radiation is 2.73° Kelvin. The variations observed
in this temperature across the night sky are very tiny.
If the cosmic microwave background is at such
a uniform temperature, it should mean that the photons have been thermalized
through repeated particle collisions. But this presents a problem with
causality in an expanding universe. Using the RobertsonWalker metric
with k=0, assuming that a(t) ~ t^{m}, the distance a photon
could have traveled since the beginning of the Big Bang at t=0 to some
other time t_{0} is given by the horizon size r_{H}(t_{0})
The power m is set by the equation of state for the energy
source under consideration, so that
For a matter or radiation dominated Universe, m=2/3 or 1/2, respectively.
Therefore the horizon size is finite, because the integral converges
as t > 0 for m<1, and it is much smaller than necessary to account
for the isotropy observed in the cosmic microwave backgound. To make
the horizon integral diverge or grow extremely large would require a
Universe that expanded more rapidly than is possible using matter or
radiation in the Einstein equations.
The horizon size predicted by the existing Big Bang
model is too small to account for the observed isotropy in the cosmic
microwave background to have evolved naturally by thermalization. So
that's the horizon problem.
Magnetic monopole problem
A magnetic monopole would be a magnet with only
one pole. In other words, it would have net magnetic charge. But magnetic
monopoles have never been observed or created experimentally. When a
magnet with a north and south pole is cut in half, it becomes two magnets,
each with its own north and south poles. There doesn't seem to be a
way to create a magnet with only one pole. Yet particle theories like
Grand Unified Theories and superstring theory predict magnetic monopoles
should exist.
In particle theory, a magnetic monopole arises from a topological
glitch in the vacuum configuration of gauge fields in a Grand Unified
Theory or other gauge unification scenario. The length scale over which
this special vacuum configuration exists is called the correlation length
of the system. A correlation length cannot be larger than causality
would allow, therefore the correlation length for making magnetic monopoles
must be at least as big as the horizon size determined by metric of
the expanding Universe.
According to that logic, there should be at least
one magnetic monopole per horizon volume as it was when the symmetry
breaking took place.
This creates a problem, because it predicts that the monopole density
today should be 10^{11} times the critical density of our Universe,
according to the Big Bang model.
But so far, physicists have been unable to find even
one.
Next:
The Inflationary Universe>>
