  In this article we follow a previously developed analytical line, based on
the application of the tools of the singular semi-Riemannian geometry, to push
the limits of general relativity (GR) beyond the big bang geometric singularity
on the spacetime manifold, to overcome this way the breakdown of cosmological
solutions. The extreme physics conditions of the first instants of the universe
are very far from our experimental and observational possibilities, thus in the
present work we follow a speculative line developing a new set of Friedmann's
equations and solutions based on the complexification of the
Friedmann-Lema\^itre-Robertson-Walker (FLRW) metric. The resulting complex
conjugated Friedmann's type equations describe two scenarios for the
evolutionary universe. In the first scenario, of the so called $branch\, cut\,
universe$, the universe evolves continuously from the negative complex
cosmological time sector $t_C$, prior to the big bang, to the positive one,
circumventing continuously a branch cut, and no primordial big bang type
singularity occurs, only branch points. In the second scenario, the branch cut
and branch point disappear after the $realization$ of complex time by means of
a Wick rotation, which is replaced here by the thermal time. In the second
scenario, the universe has its origin in the big bang, but the model
contemplates simultaneously a mirrored parallel evolutionary universe going
backwards in the cosmological thermal time negative sector.
