  Branch-cut gravity (BCG) is an extended version of the ontological domain of
General Relativity, which is analytically continued to the complex plane. When
combined with the Hawking-Hertog multiverse conception, BCG successfully
addresses the issue of the primordial singularity. It consistently portrays the
early Universe as a Riemannian foliation in which the singularities of the
multiverse merge, giving rise to a smooth branching topological structure that
resembles continuously connected Riemann surfaces. This structure introduces a
new cosmic scale factor that is analytically continued into the complex plane.
In this contribution, we start with the recently developed Wheeler
DeWitt-Horava-Lifshitz non-commutative BCG formulation of quantum gravity. We
investigate the impact of a non-commutative mini-superspace of variables
obeying Poisson algebra on the accelerated behavior of the branch-cutting
cosmic scale factor. drive spacetime acceleration, offering a new perspective
on explaining the accelerating expansion rate of our Universe. As far as
primordial relic gravitational waves are concerned, our predictions reveal an
intricate transition between the two phases of the branched Universe: a
contraction phase preceding the conventional concept of a primordial
singularity and a subsequent expansion phase whose transition region is
characterized by a Riemannian topological foliation structure. Furthermore,
this transition is characterized by asymmetric distributions of gravitational
wave intensities.
