The Big Bang Theory is the dominant theory in cosmology about the early development of the universe. According to this theory, the universe emerged spontaneously between 10 and 20 billion years ago. The universe was initially microscopic, and almost uniformly filled with energy. As the universe rapidly grew, the temperature dropped, leading to the creation of the known forces of physics, elementary particles, and eventually hydrogen and helium atoms. Over time, these (almost) uniformly-distributed atoms were pulled together by gravity into clumps, forming stars, galaxies, and the other structures seen today.
The Big Bang was not an explosion of matter moving outward to fill an empty universe. Instead, it involved the rapid growth of the universe itself. Because it involves the universe itself expanding, distant galaxies can actually move apart faster than the speed of light. This is possible because relativity only states that information cannot travel faster than the speed of light.
In 1927, the Belgian priest Georges Lemaître was the first to propose that the universe began with the explosion of a primeval atom. His proposal came after observing the redshift in distant nebulae by astronomers to a model of the universe based on relativity. Years later, Edwin Hubble found experimental evidence to help justify Lemaître's theory. Hubble determined that distant galaxies in every direction are receding (with regard to the Earth) at speeds directly proportional to their distance.
Since galaxies were receding, this suggested two possibilities. One that was suggested by Gamow was that the universe begin at a finite time and has been expanding ever since. The other was Fred Hoyle's steady state model in which new matter would be created as the galaxies moved away from each other and that the universe at one point in time would look roughly like any other point in time. For a number of years the support for these two opposing theories was evenly divided.
In the intervening period however, all observational evidence gathered has provided overwhelming support for the Big Bang Theory, and since the mid-1960's it has been regarded as the best available theory of the origin and evolution of the Cosmos. The Big Bang Theory is not without weaknesses (discussed below), and these have been the focus of the handful of cosmologists who still support non-standard cosmologies. Regardless, the Big Bang Theory is the hypothesis most strongly supported by the evidence, and it is unlikely to be supplanted until such a time as a new theory provides a "better fit".
The Big Bang Theory and the supporting evidence
The Redshift of galaxies and distribution of quasars
By analyzing the light from distant galaxies, one notices that the shape of the light's spectrum is very similar, but the whole spectrum is shifted to longer wavelengths for galaxies farther away. This suggests that the galaxies are moving away from us, resulting in an effect akin to the Doppler effect called redshift.
Quasars are predicted to only be possible in the early stages of a dynamic cosmos by BBT, and observation evidence supports this, as more quasar population becomes denser the further away one looks. (more needed)
A (now) major aspect of the Big bang hypothesis was the prediction in the 1940's of cosmic microwave background radiation or CMBR. The theory proposed that, as all the mass/energy of the universe emerged from the primordial explosion, the initial density of the universe was incredibly high, and hence the temperature of the universe must have been extremely hot (as matter gets hotter when compressed to a higher density). The initial temperature of the universe was so high that matter (as we know it could not exist) as the subatomic particles were too energetic to aggregate into atoms.
However, as the universe was expanding it must have also cooled. As the temperature of the universe fell, matter could form from the primordial plasma. The theory predicted that at some stage (currently reckoned to be around 500 000 years after the beginning), this plasma would thin out sufficiently to permit photons to be set free from the attraction of the other matter, and travel through the constantly expanding reaches of space. The process that produced this inconceivable blast of free energy is known as photon decoupling.
Based on this premise, the theory predicted that this massive blast of radiation should have left some traces in the cosmos, and would have a number of properties. Essentially it says that at the universe was extremely hot at one point, it should still be a little bit warm even today, and calculations predicted a residual tempreature of about 3K (3 degrees above absolute zero). Additionally, as the radiation was produced simultaneously, the traces of it should be uniform or isotropic. Another prediction was that as these photons are subject to the expansion of space, their wavelengths would have been "stretched" or red-shifted. A critical further prediction was that the further away one looks, the hotter the universe should appear to be (as looking further away corresponds to looking backwards in time), and at some extremely distant point the radiation in the universe should be so thick as to become opaque.
At the time they were made, the predictions of the Big Bang theory regarding CMBR were largely ignored, simply because they remained unverifiable due to inadequate technology for nearly 20 years. However, in 1964, Arno Penzias and Robert Wilson conducted a series of observations using a self-assembled microwave receiver. Their findings provided substantial confirmation of almost every aspect of the CMBR predictions, and overwhelmingly swayed the balance of opinion in favour of the Big Bang hypothesis. Penzias and Wilson were awarded the Nobel Prize for this discovery. In 1989, NASA launched the Cosmic Background Explorer satellite (COBE), and the initial findings (released in 1990) were a stunning endorsement of the Big Bang predictions regarding CMBR, finding a local residual temperature of 2.726 K, determining that the CMBR was indeed isotropic, and confirming the "haze" effect as distance increased.
Matter distribution and concentration in the cosmos
Using the big bang model it is possible to calculate the concentration of helium in the universe. Steady State Theories fail to account for the volume of deuterium in the cosmos, because Deuterium is easily destroyed in stars and there are no known astrophysical processes other than the big bang itself that can produce it in large quantities. Hence the fact that deuterium is not a rare component of the universe suggests that the universe has not been around forever.
One piece of evidence for the Big Bang model is that it resolves Olber's Paradox of why the sky is black at night. See Olber's paradox.
Weaknesses and criticisms of the Big Bang Theory
One weakness of the big bang theory is the obvious question of how the big bang occurred. The difficulty of answering this question lies with the absence of a theory of quantum gravity. As one goes back in time, the temperature and the pressures increase to the point where the physical laws governing the behavior of matter are unknown. It is hoped that as we understand these laws that we will better be able to answer the question of what happened "before" the big bang.
Dark matter problems
Age of universe and values of omega, Hubble Constant.
The Future Under the Big Bang Theory
All the matter in the Universe is gravitationally attracted to each other. This should cause the expansion rate of the Universe to slow down over time. Exactly how much matter exists, relative to how large the Universe is and how fast it is currently expanding can lead to one of three scenarios:
The Big Crunch
If the gravitational attraction of all the matter in the Universe is high enough, it could stop the expansion of the Universe, and then reverse it. The Universe would then contract, in about the same time as the expansion took. Eventually, all matter (and energy?) would be compressed back into a single point. It is unknown what would happen after this, perhaps a new Universe would be formed in another Big Bang.
The Big Freeze
If the gravitational attraction of all the matter in the Universe is low enough, the expansion will never stop. As the matter disperses into ever greater and greater volumes, new star formation would drop off. The average temperature of the Universe would asymptotically approach absolute zero, and the Universe would become very still and quiet. Eventually, all the protons would decay, and the Universe would consist of dispersed subatomic particles.
If the gravitational attraction of all the matter in the Universe is just right, the expansion of the Universe will asymptotically approach zero. The temperature of the Universe would asymptotically approach a stable value slightly above absolute zero. The end result (with protons decaying) would be similar to the Big Freeze.