Based on observation of the uniform expansion of the universe (Hubble constant), the Big Bang is a relatively simple concept:

1.  At t=0, an extremely dense, small patch of energy explodes because of the repulsive nature of the elementary forces.

2.  Equilibrium cooling takes place until present time, with matter condensing from energy as the temperature decreases.

3.  Depending on the quantity of energy/matter it started with, the universe will be either open, closed, or flat. (Open: it will expand forever. Closed: it will expand, slow down, and then fall back on itself. Flat: it will expand until it reaches some fixed equilibrium size where it stays forever.)

Note: Although the word explodes is commonly used with respect to the Big Bang, it is not strictly correct. In an explosion, particles at the center fly apart due to a impulse force but immediately began to slow down, so that particles far away from the center move slower than particles near the center. This is what you see in a 4th of July skyrocket. In the Big Bang, the forces are applied continuously to all particles, so that particles far away from the center are moving faster. This is what was measured by Hubble.
 

NASA's Cosmic Background Explorer (COBE) satellite launched in 1989 measured the radiation left over from the big bang explosion. This radiation is isotropic (the same in all directions) within one part in one hundred thousand. The classic discovery plot is shown below in false color. Light blue indicates a median value, red is median plus 1/100,000, and dark blue is median minus 1/100,000.
 

What the universe looked like 200,000 years after the Big Bang

 

What the Universe looks like now.  This is a slice of the sky that contains 1074  galaxies!!  Notice the huge clusters of galaxies and the enormous voids.

Small-scale inhomogeneity: if everything was homogeneous in the initial moments of time, why did galaxies condense?

Why did clumps of stars combine out of a homogeneous energy distribution at seemingly arbitrary locations? This Hubble Space Telescope photograph is a beautiful visual example of reality:

Flatness/Oldness: Humans prefer a value of Omega = 1; i.e., a flat universe. Experiments are pointing in the same direction. This is sometimes called the "Oldness Problem," for if Omega is very much larger than 1, the universe would have collapsed on itself a long time ago and we would not be here now! It seems unusual that nature would select such a delicate equilibrium point; is there some reason that Omega = 1 is preferred?

Size of the Universe as a Function of Time for 3 values of Critical Mass Density

(a) Omega <1 (b) Omega = 1 (c) Omega > 1

No one has discovered naturally occurring anti-matter or magnetic monopoles, yet nothing in the theory suggests that matter and anti-matter shouldn't occur in equal proportions, nor that magnetic monopoles shouldn't exist.

1.  At T < 0, the universe sits on the central plateau of the field given on the previous page. It may have been there for a very long time, since this is a true equilibrium point.

2.  Eventually, at T = 0, quantum fluctuations start the universe "rolling" off the plateau. This is called the slow rollover period. Nothing marks the point T = 0 as unusual or different from the time before it or immediately after.

3.  As the universe reaches the edge of the plateau, it rapidly falls down the side, dumping an enormous quantity of energy originally stored in the field into the universe. This happens so fast that the universe cannot heat up adiabatically (in equilibrium) as would a classic system. (This is often called reheating.) Instead, it expands by a factor of approximately 3 x 10⁴³. This is the Inflationary period. During this period, the forces go through a "phase transition", where the single unified force transitions into the multiple forces we know today. This is called a phase transition because it is similar to water vapor at high temperature and pressure where only the vapor phase can exist; as it cools liquid water, then solid ice can exist.

4.  Finally, the universe evolves as originally described by the Standard Big Bang model. The various particles condense from the energy field; then atoms, and finally molecules come into being. Quantum fluctuations from the universe rolling back and forth inside the trough of the field minimum cause additional energy to build up in certain random parts of space where galaxies form.

How Inflation Addresses the Problems with the Standard Model

1.  Smoothness - extreme expansion evens out the energy distribution.

2.  Galaxy formation - quantum fluctuations in field give matter clumps.

3.  Flatness - The mathematics of inflation drive Omega to 1 (at least to within 100 which is close enough!) independent of initial mass density.

4.  Undiscovered Relics - Volume expansion makes monopoles rare. Supersymmetry predicts matter-antimatter ratio of 3/1.

Inflation also helps with the problem of multiple dimensions in Superstring theories. Suppose that inflation only happened in the 3 dimensions we know today; then the other dimensions would be so small that we can't see them.

How Can Inflation be Observed?

1.  Relic anti-matter and monopoles should not exist. So far, they don't.

2.  In Dark Matter (Evidence for and possible candidates):

4.  By new measures of the abundance of light elements. Unfortunately, this measures baryonic mass only.

5.  By making a ``Build-it-yourself'' universe in the lab. This is not as impossible as it might seem.

Even More Exotic Theories

Believe it or not, people at prestigious universities get paid to think about this stuff! One even wrote a book that made it to the New York Times best seller list, but was probably the most un-read book ever there.