The Big Bang theory describes cosmology, scientists' theory for how the Universe has evolved. The theory hypothesizes that the Universe was once nearly-infinitely dense, and compressed into a tiny point. Matter as we know it did not exist; the Universe was so hot that matter was indistinguishable with energy. Then, something then caused the Universe to expand. This is the Big Bang, which marks the point at which the theory can begin to accurately describe the Universe.
The evolution of the Universe is determined by the fact that as the Universe expands, it cools. The first accurate calculations in the theory start around a trillionth of a second after the Big Bang. For the next 10 seconds, matter &mdash protons, neutron, and electrons &mdash formed out of a quark-gluon plasma (see the Standard Model. This soup persisted for several minutes, and then between 3 and 20 minutes after the Big Bang, ions of hydrogen, helium, and lithium formed. The Universe was then dominated by a plasma, in which electrons, ions, and photons continuously interacted.
At this point, things slow down, and over the course of a few hundred thousand years, the Universe cools to the point that electrons can combine with ions. When this happens, photons cease interacting with the newly-neutral atoms, and can start moving freely through space. This point in time is visible to us as the cosmic microwave background. Since about 300,000 years after the big bang, this background radiation has cooled as the universe expanded, from temperatures of 3,000° K, to its current temperature of about 2.7° K.
Over the course of the next hundred million years or so, regions of the Universe that were slightly more dense than their surroundings began to collapse under the force of Gravity. These dense regions formed stars, which were aggregated into galaxies, which in turn collected into large clusters of galaxies. Their light illuminated the Universe, splitting atoms back into the plasma that now fills most of the space between stars. Thus, the Universe as we see it now came into being.
With the realization that the Universe was expanding, physicists began to contemplate, "What is it expanding from?" Looking back in time, the expanding Universe would have had to have been very small in some time in the finite past. This idea explained two more things that astronomers had long been puzzling about.
First, after Hubble demonstrated that galaxies were were collections of stars like our Milky Way, it was realized that the Universe remarkably uniform, with similar galaxies punctuating the empty void of space as as far as telescopes could grasp light. If the Universe had expanded from a small, dense state, it would explain why it now looked so homogeneous.
Second, astronomers had long been noted that if the Universe were infinitely old and static (not expanding), one would expect to see starlight coming from every point on the sky. This would make the sky appear uniformly bright, shining with the intensity of the surface of the Sun. This was referred to as Olber's paradox, because the sky is most certainly dark at night. The only solutions to the paradox that obey the known laws of physics (which excluded suggestions that light could disappear) are that the Universe is expanding, that the Universe is not old enough for starlight to have filled it, or both. These last two cases are exactly what the Big Bang theory predicts.
In the 1940s, astronomers began to consider implications of one of the key hypotheses of the Big Bang theory: that the Universe was once compressed nearly to a point. Throughout the 1940s, George Gamow and collaborators worker out that the left-over heat from when the Universe was young should still be visible in the sky. This turned out be the case. Coincident with the theoretical work, and for several decades following, several experiments found this radiation. Studies of cyanide molecules by Andrew McKellar suggested that space had an effective temperature of 2.3 K, while experiments to measure microwave radiation found a persistent signal with an apparent of about 3 K. However, it wasn't until 1965 that several scientists realized that these observations actually revealed the left-over energy from the Big Bang. This provided the theory's first major verified prediction.
Further calculations of the conditions in the early Universe were able to predict which elements would have formed within the first 20 minutes after the Big Bang. The models successfully predict the relative amounts of hydrogen, deuterium (an isotope of hydrogen in which a neutron is included with the proton), two isotopes of helium, and lithium in the Universe..
The fact that the Universe is expanding and aging has been confirmed by several observations. The temperature of the microwave background can be tracked over billions of years by measuring the energy of carbon atoms. These observations confirm the Universe was hotter in the past. Astronomers have confirmed that the Universe has expanded, by determining the density of galaxies used to be higher when the Universe was younger. Finally, the Big Bang theory predicts that time should appear to pass slower when looking at distant objects. This has been confirmed by observations that more distant supernovae take longer to fade.
The Big Bang theory makes clear predictions for the structure of the Universe, and yet, combined with observations from other fields, astrophysicists have been left with some vexing problems. First, observations of galaxies, clusters of galaxies, and the cosmic microwave background all suggest that the Universe contains much more matter than we see emitting light. This matter is identifiable because it interacts gravitationally with other objects, but because it emits no light, it is called dark matter. Dark matter makes up about a quarter of the Universe, yet we do not know what it is.
Moreover, observations that use supernova to determine the distances to galaxies suggest that the Universe is currently accelerating. This implies that there is some force counter-acting gravity, which astronomers now refer to as dark energy. Dark energy makes up 70% of the Universe, but, again, physicists have no idea what it is.
Physicists also do not understand the early phases of the Big Bang, the first millionth of a second of the Universe. The Standard Model of particle physics is untested for matter as hot and dense as it would have been at that time. There are two big puzzles. One is that the smoothness of the Universe suggests that it underwent a period of exponential expansion, referred to as Inflation. The other is that shortly after the Big Bang, matter and anti-matter should have been about equally abundant. Somehow, when the matter and anti-matter annihilated, there was still left-over ordinary matter, which we now see in the Universe. It is not known what caused either of these things, but they might be understandable under a theory that would unify the fundamental forces (electromagnetic, weak, strong, and gavtiational).
Finally, physicists do not know what will happen to the Universe in the distant future. When I was a child, astrophysicists were wondering whether the Universe would expand forever, or collapse back in upon itself in a Big Crunch. A decade ago, in the wake of COBE and the Hubble Space telescope, but before Dark Energy was needed in cosmology, we were convinced that the Universe would continue expanding forever. However, astrophysicists now have to consider the notion that Dark Energy would take over, and rip the Universe apart.
Ned Wright has one of the best cosmology sites, which is an interesting mix of introduction and technical information. Check out the Frequently Asked Questions in particular.
The Usenet Physics FAQ is another excellent reference, for all sorts of things.
Niel deGrasse Tyson wrote another nice description of cosmology.
Like science itself, these pages are under construction. OK, so they are in a lot worse shape than science. I welcome your comments.