Astronomy & Cosmology
The fundamental issue with any cyclic model is the second law of thermodynamics, which, basically, states that entropy always increases. This results in the cycles having to be longer and longer each time the Universe contracts, and bounces. Looking backwards, therefore, the cycles must have been shorter and shorter, implying that there must have been a beginning which is exactly what cyclic models are trying to avoid! The Steinhart-Turrok model uses dark energy and colliding branes to avoid the issue. Baum and Frampton take a somewhat different approach.
The equation of state is equal to the ratio of pressure to energy density. For the Universe, it has been calculated at approximately -1, ± a very small amount. Baum and Frampton assume a value for the equation of state for the dark matter in the Universe that is less than -1. Ordinarily, this would lead to the Universe ending in what is known as the Big Rip, which I discuss in the next section. Baum and Frampton suggest that in an instant just before the Big Rip, in fact less than 10-27 seconds before the rip, space turns around and splits into a huge number of independent volumes. These volumes of space essentially correlate to "observable universes" or causally related volumes, which have contracted to a very small size due to the exponential expansion. Each of these volumes then contracts by an enormous amount, perhaps down to the Planck length. Because each volume of space contains no matter or energy due to the build up to the Big Rip, the entropy in any individual volume of space reduces almost to zero, and remains virtually unaltered through the contraction. Thereafter, the pattern roughly follows the Big Bang scenario with entropy increasing again through cosmic inflation and on into the creation of the universe. Remember; this happens in each "piece" of space derived from the original universe, and results in an extraordinarily large, but finite, number of new universes.
There are lots of neat aspects to this theory, not least of which is the idea that so many new universes are created at the end of each cycle, that it is no surprise that there is a Universe in which life like ours can evolve. My only difficulty with it is the look back dilemma. A universe produces a very large, but finite, number of "new universes". However, the original universe was on of a very large, but finite, number of universes produced in the previous cycle. As we look back, the total number of universes is decreasing, implying that at some point there must have been an original, primæval universe. This begs the question of what came before that original Universe, so we are back to our dilema.
The Baum-Frampton Cyclic Model