Conformal Cyclic Cosmology (CCC) is a concept proposed in 2006 by the Nobel Prize winning cosmologist Professor Roger Penrose. It attempts to resolve a paradox associated with (standard) Big Bang theoryplugin-autotooltip__plain plugin-autotooltip_bigBig Bang theory

There is now a large body of evidence (from different sources) to support the Big Bang Theory for the origin of the universe, but the problem remains as to the origin of the material or energy which initialised it.

As the UK’s Astronomer Royal Martin Rees has put it :.

The issue arises from one of the most fundamental principles of physics: the Second Law of thermodynamics. According to the Second Law, roughly speaking, the entropy of the universe increases with time, where the term 'entropy' refers to an appropriate measure of disorder or lack of 'specialness' of the state of the universe. Since the entropy increases in the future direction of time, it must decrease in the past time-direction. Accordingly, the initial state of the universe must be the most special of all, so any proposal for the actual nature of this initial state must account for its extreme specialness."

Source :Roger Penrose, Proceedings of EPAC 2006, Edinburgh, Scotland

The paradox being - where did this universal concentration of 'specialness' come from?

Penrose's CCC conjecture is that the ultimate fate of the Universe is that, given enough time, all the fundamental particles - including protons and (even) electrons - will eventually decay into photons. In other words pure energy. At this point, Penrose argues, time becomes not only a meaningless concept, but also disappears as a physical reality : "[…] the universe has no way of 'building a clock' " The concept of 3D space would also be meaningless.

Because time does not exist and the Universe essentially occupies no space, the paradox described above is resolved - allowing for the (next) Big Bang.

Note: The last paragraph of Penrose's paper points out that : "The details of all this have yet to be worked out, […] "