  We wonder if a cyclic universe may be dominated alternatively by matter and
antimatter. Such a scenario demands a mechanism for transformation of matter to
antimatter (or antimatter to matter) during the final stage of a big crunch. By
giving an example, we have shown that in principle such a mechanism is
possible. Our mechanism is based on a hypothetical repulsion between matter and
antimatter, existing at least deep inside the horizon of a black hole. When
universe is reduced to a supermassive black hole of a small size, a very strong
field of the conjectured force might create (through a Schwinger type
mechanism) particle-antiparticle pairs from the quantum vacuum. The amount of
antimatter created from the vacuum is equal to the decrease of mass of the
black hole and violently repelled from it. When the size of the black hole is
sufficiently small, the creation of antimatter may become so fast, that matter
of our Universe might be transformed to antimatter in a fraction of second.
Such a fast conversion of matter into antimatter may look as a Big Bang. Our
mechanism prevents a singularity; a new cycle might start with an initial size
more than 30 orders of magnitude greater than the Planck length, suggesting
that there is no need for inflationary scenario in Cosmology. In addition,
there is no need to invoke CP violation for explanation of matter-antimatter
asymmetry. Simply, our present day Universe is dominated by matter, because the
previous universe was dominated by antimatter.
