In Conformal Cyclic Cosmology the universe iterates through infinite cycles, with the future timelike infinity of each previous iteration being identified with the Big Bang singularity of the next.
Conformal Cyclic Cosmology (CCC) was put forward by one of Roger Penrose and his colleagues in 2005 as a possible theoretical scheme that could account for the strange imbalance between the apparently thermal nature of matter and radiation in the early universe, as opposed to the very low gravitational entropy, as evidenced by the universe’s initial uniformity and suppression of gravitational degrees of freedom. In CCC, this comes about from our big bang having been the conformal continuation of the remote future of a previous aeon whose own big bang had arisen from an aeon prior to that, etc., and the suppression of initial gravitational degrees of freedom at the big bang of each aeon is a conformal consequence of this. Likewise, our own aeon’s remote future conformally continues to become the big bang of a succeeding aeon, and so on.
It is argued that the crossover from aeon to aeon is physically plausible, despite the enormous differences in densities and temperatures at each crossover 3-surface X, because the physics on both sides of X is dominated by conformally invariant processes carried out by effectively massless particles: at each big bang, by particles whose kinetic energy totally dominates their mass, and at each aeon’s remote future by photons. Black holes eventually disappear by Hawking evaporation.
A paper by Roger Penrose, Daniel An, and Krzysztof A. Meissner presents powerful observational evidence of anomalous individual points in the very early universe that appear to be sources of vast amounts of energy, revealed as specific signals found in the CMB sky. Though seemingly problematic for cosmic inflation, the existence of such anomalous points is an implication of conformal cyclic cosmology (CCC), as what could be the Hawking points of the theory, these being the effects of the final Hawking evaporation of supermassive black holes in the aeon prior to ours. Although of extremely low temperature at emission, in CCC this radiation is enormously concentrated by the conformal compression of the entire future of the black hole, resulting in a single point at the crossover into our current aeon, with the emission of vast numbers of particles, whose effects we appear to be seeing as the observed anomalous points. Remarkably, the B-mode location found by BICEP 2 is at one of these anomalous points.