The predictions of General Relativity suggest a universe in which, as we follow time backward, the hotter and the more dense it was, and the more rapidly it was expanding and that, around 13.7 billion years ago, at the extreme gravitational regime of its evolutionary process, the density, temperature, and expansion rate of the universe would start off as infinite. The General Relativity prediction of a singularity in the early universe would impose a limitation to our understanding of the cosmos and gravity, implying loss of logic and of formal consistency and predictability, making it impossible to impose initial conditions. These extreme conditions of the initial state of the universe are very far from our experimental possibilities, and presently, theoretical models allow only speculations about the avoidance of physical singularities or about the physical conditions that circumvented this drastic consequence of General Relativity. Speculations aside, in this study, we follow an analytical line in which we apply the tools of singular semi-Riemannian geometry to push the limits of General Relativity beyond the Big Bang singularity.

In this contribution, we identify two scenarios for the evolutionary branch cut universe. In the first scenario, the universe evolves continuously from the negative complex cosmological time sector, prior to a primordial singularity, to the positive one, circumventing continuously a branch cut, and no primordial singularity occurs in the imaginary sector, only branch points. In the second scenario, the branch cut and branch point disappear after the realization of the imaginary component of the complex time by means of a Wick rotation, which is replaced 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.A quantum formulation based on the Wheeler-DeWitt equation is sketched and preliminary conclusions are drawn.

In this article, we follow a previously developed theoretical approach, based on the tools of the singular semi-Riemannian geometry, to push the limits of time beyond the primordial spacetime singularity. By complexifying the Friedmann-Lemaître-Robertson-Walker (FLRW) metric and Friedmann's equations, we model a branch cut universe, in which the cosmic FLRW metric scale factor is analytically continued to the complex plane, and becomes equivalent from a conceptual point of view of describing a hypothetical general metric of maximally symmetric and homogeneous superposed multiple universes.

In this contribution to the Festschrift for Prof. Remo Ruffini, we investigate a formulation of quantum gravity using the Hořava–Lifshitz theory of gravity, which is General Relativity augmented by counter-terms to render the theory regularized. We are then led to the Wheeler–DeWitt (WDW) equation combined with the classical concepts of the branch-cut gravitation, which contemplates as a new scenario for the origin of the Universe, a smooth transition region between the contraction and expansion phases. Through the introduction of an energy-dependent effective potential, which describes the space-time curvature associated with the embedding geometry and its coupling with the cosmological constant and matter fields, solutions of the WDW equation for the wave function of the Universe are obtained. The Lagrangian density is quantized through the standard procedure of raising the Hamiltonian, the helix-like complex scale factor of branched gravitation as well as the corresponding conjugate momentum to the category of quantum operators. Ambiguities in the ordering of the quantum operators are overcome with the introduction of a set of ordering factors α, whose values are restricted, to make contact with similar approaches, to the integers α=[0,1,2], allowing this way a broader class of solutions for the wave function of the Universe. In addition to a branched universe filled with underlying background vacuum energy, primordial matter and radiation, in order to connect with standard model calculations, we additionally supplement this formulation with baryon matter, dark matter and quintessence contributions. Finally, the boundary conditions for the wave function of the Universe are imposed by assuming the Bekenstein criterion. Our results indicate the consistency of a topological quantum leap, or alternatively a quantum tunneling, for the transition region of the early Universe in contrast to the classic branched cosmology view of a smooth transition.

The field equations of the pseudo‐complex general relativity (pc‐GR) have an extra term, of repulsive character, which may halt the gravitational attractive collapse of matter distributions in the evolution process of compact stars. This additional term simulates the presence of dark energy in the Universe. In this paper, we explore the presence of this additional term and study the role of dark energy in the structure of neutron stars composed by nucleons, hyperons, mesons, and weakly interacting massive fermion dark matter particles (WIMPs) held together by the nuclear force and the gravitational interaction superimposed on the repulsive background of dark energy. To describe the hadron–lepton sector, we consider three different effective models, Zimanyi–Moszkowski, Boguta–Bodmer, and the analytic parameterized coupling model, which we extend to consider, in the baryonic sector, the presence of the whole fundamental baryon octet. By solving the Tolman‐Oppenheimer‐Volkoff (TOV) equations, we estimate the maximum gravitational mass of neutron stars.