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An atrist's view of the Big Bang in progress. Image courtesy Particle Physics Laboratory at Annecy-le-Vieux, France
The theory was first proposed by Georges Lamaitre. He referred to it as the hypothesis of the primeval atom. He based his work on the theories of great mathematicians and physicists; Albert Einstien, Edwin Hubble, and Alexander Freidman, in particular. In 1927 he proposed that that the distances to far away galaxies were generally proportional to their redshifts(the appearance that an object is redder than it would appear to a hypothetical observer both closer to it and at rest relative to it ). This proposition was confirmed by Edwin Hubble in 1929. Scientists took this to indicate that all very distant galaxies and clusters have an apparent velocity going directly away from our vantage point: the farther away, the higher the apparent velocity. If the distance between galaxy clusters is increasing today, everything must have been closer together in the past. This idea has been considered into extreme densities and temperatures. Large particle accelerators have been built to test such conditions, resulting in significant confirmation of the theory within the scope of the limitations of these accelerators. The big bang does not attempt to prove the initial condition of the universe, but what happened afterward.
With great care, scientists have developed a time line for the big bang. They began by extrapolating the expansion of the universe backwards in time. The theory of general relativity yields an infinite density and temperature at a definite time in the past. This singularity signals the breakdown of general relativity. Many scientist debate how closely we can extrapolate to the singularity, but probably not earlier than the Planck era(the earliest period of time in the history of the universe, from zero to approximately 10-43 seconds Planck time, during which quantum effects of gravity were significant). The earliest, dense hot phase is considered the big bang which is considered the birth of our universe. Based on measurements of the expansion using type 1a super novae(a sub-category of cataclysmic variable stars that result from the violent explosion of a white dwarf star), measurements of temperature fluctuations in the cosmic microwave background, and measurements of the correlation function of galaxies, the universe has a calculated age of 13.73 billion years.
More recently, some scientists have based their theories of how and when the Universe will end on the big bang. Many believe that the continued expansion of the Universe will lead to a ripping apart of all matter on the molecular level at a point several billions of years off.
This is the NASA page about the big bang theory. Here on Universe Today we have a great article about the theory. Astronomy Cast offers a good episode about the large scale structure of the Universe.
Sources: NASA, ESA, NASA Science
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