I always thought C3 was strange since each cycle expands greatly in space. The size of any new cycle is vastly bigger, making C3 insensible to me. Anyhow, the

I always thought C3 was strange since each cycle expands greatly in space. The size of any new cycle is vastly bigger, making C3 insensible to me. Anyhow, the absence of strong dark energy makes things very easy for Penrose for the general concept of a cyclical universe. If gravity wins against dark energy, then a big crunch is easy, following which a new cycle starts. If instead gravity stays balanced with dark energy, then black holes slowly evaporate into photons anyway, preserving C3.