Cyclic multiverses
  Using the idea of regularisation of singularities due to the variability of
the fundamental constants in cosmology we study the cyclic universe models. We
find two models of oscillating and non-singular mass density and pressure
("non-singular" bounce) regularised by varying gravitational constant $G$
despite the scale factor evolution is oscillating and having sharp turning
points ("singular" bounce). Both violating (big-bang) and non-violating
(phantom) null energy condition models appear. Then, we extend this idea onto
the multiverse containing cyclic individual universes with either growing or
decreasing entropy though leaving the net entropy constant. In order to get an
insight into the key idea, we consider the doubleverse with the same
geometrical evolution of the two "parallel" universes with their physical
evolution (physical coupling constants $c(t)$ and $G(t)$) being different. An
interesting point is that there is a possibility to exchange the universes at
the point of maximum expansion -- the fact which was already noticed in quantum
cosmology. Similar scenario is also possible within the framework of
Brans-Dicke theory where varying $G(t)$ is replaced by the dynamical
Brans-Dicke field $\phi(t)$ though these theories are slightly different.
