The fundamental properties of the Universe, summarized above, one can
develop a simple model for the evolution of the Universe.  This model
is called the Big Bang.

The essential description of the Big Bang model is that it predicts
the Universe was hotter and denser in the past.  For most of the 20th
century, astronomers argued about the best description of the
Universe.  Was the BB right? or was another model better?  Today, most
astronomers think that the BB is essentially correct, the Universe was
hotter and denser in the past.  Why?

When Einstein was working on his theory of gravity, around 1915, he
was horrified to discover that it predicted the Universe should either
be expanding or collapsing.  The prevailing scientific view at the
time was that the Universe was static, it always had been and always
would be.  He ended up modifying his theory, introducing a long-range
force that cancelled gravity so that his theory would describe a
static Universe.

When Hubble announced that galaxies were receding from us, astronomers
realized quickly that this was consistent with the notion that the
Universe is expanding.  If you could imagine "running the clock
backwards" and looking into the past, you would see galaxies getting
closer together.  In effect, the Universe would be getting denser.

If the Universe was denser in the past, then it was also hotter.  At
some point in the past, the conditions in the Universe would have
resembled the interior of a star.  If so, we should expect that
nuclear fusion would occur.  Detailed predictions of how much nuclear
fusion would have occurred in the early Universe were first undertaken
by George Gamow and his collaborators.  Since then, the calculations
have been refined, but the essential result is still the same.  After
nuclear fusion stopped, about 1000 seconds into the Universe's
history, there should be about one Helium-4 atom for every 10 Hydrogen
atoms, one Deuterium atom (heavy hydrogen) for every 10,000 H atoms,
one Helium-3 atom for every 50,000 H atoms, and one Lithium-7 atom for
every 10 billion H atoms.  These predicted abundances are in very good
agreement with the observed abundances.

As the Universe expanded and cooled, the radiation in it should have
also lost energy.  In 1965 Arlo Penzias and Robert Wilson were annoyed
to discover that no matter what direction they pointed a telescope,
they kept picking up faint glow.  Some physicists at Princeton
recognized that this faint glow was exactly what was expected from a
cooling Universe.  Since then, the COBE satellite has measured the
temperature of this radiation to be 2.728 +/- 0.002 K.  

It is the combination of these excellent agreements between prediction
and observation that lead most astronomers to conclude that the Big
Bang is a good model for describing the Universe.