Pushing the limits of General Relativity beyond the Big Bang singularity

Abstract

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.

Pushing the limits of time beyond the Big Bang singularity: Scenarios for the branch cut universe

“…These conceptions present some points of contact with a line of thought we recently developed (Vasconcellos et al, 2020(Vasconcellos et al, , 2021 where we applied the tools of singular semi-Riemannian geometry to push the limits of general relativity and time beyond a primordial singularity, giving rise to a branch cut universe. In this contribution, we sought to identify evolutionary scenarios for the branch cut universe.…”

Pushing the limits of time beyond the Big Bang singularity: The branch cut universe

“…equations. In a visualization of ln[ (t)] shown in Vasconcellos et al (2020), the Riemann surface appears to describe a spiral curve around a vertical line corresponding to the origin of the complex plane (see the left panel of Figure 1). In the right panel of Figure 1, we extended the graphical representation of the previous article showing the real part of this function, where some of the multiverses are represented.…”

“…The deduction of the complex Friedmann's-type equations was carried out through the following simple canonical steps (Vasconcellos et al 2020):…”

“…Due to the nonlinearity of Einstein's equations, such a direct generalization would not be formally consistent. The present formulation as stated earlier, is the outcome of complexifying the FLRW metric and results in a sum of equations associated to infinitely many poles (in tune with Hawking's assumption of infinite number of primordial universes that occurred simultaneously) arranged along a line in the complex plane with infinitesimal residues (for details, see Vasconcellos et al (2020)). The multiverse conception corresponds here to a theoretical mathematical device for implementation of the proposal.…”

“…In a search to overcome the presence of singularities in general relativity, we have combined in a recent publication (Vasconcellos et al 2020) the multiverse proposal by S. Hawking and T. Hertog of a hypothetical set of multiple universes, existing in parallel (Hawking & Hertog 2018) and the technique of analytical continuation in complex analysis applied to the Friedmann-Lemaître-Robertson-Walker (FLRW) metric. As a result, we obtained Friedmann-type equations for a complex version of the ΛCDM (Λ ≠ 0) model:…”