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What came before the Big Bang?

   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:

Radiation dominated Universe

   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

Flatness problem

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 radiation-dominated 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 Robertson-Walker metric with k=0, assuming that a(t) ~ tm, the distance a photon could have traveled since the beginning of the Big Bang at t=0 to some other time t0 is given by the horizon size rH(t0)

Horizon problem

   The power m is set by the equation of state for the energy source under consideration, so that

Equation of state and scale factor

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.

Big Bang monopole density

This creates a problem, because it predicts that the monopole density today should be 1011 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>>

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Black Holes

A magnet cut in half still has two poles

Magnets only come with two poles, and this tells us about the early Universe.

How old is the Universe? // Structure of the Universe // The Big Bang // Before the Big Bang? // What about string theory?

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