Through the Big Bang

Abstract: All measurements are comparisons. The only physically accessible degrees of freedom (DOFs) are dimensionless ratios. The objective description of the universe as a whole thus predicts only how these ratios change collectively as one of them is changed. Here we develop a description for classical Bianchi IX cosmology implementing these relational principles. The objective evolution decouples from the volume and its expansion degree of freedom. We use the relational description to investigate both vacuum dominated and quiescent Bianchi IX cosmologies. In the vacuum dominated case the relational dynamical system predicts an infinite amount of change of the relational DOFs, in accordance with the well known chaotic behaviour of Bianchi IX. In the quiescent case the relational dynamical system evolves uniquely though the point where the decoupled scale DOFs predict the big bang/crunch. This is a non-trivial prediction of the relational description; the big bang/crunch is not the end of physics - it is instead a regular point of the relational evolution. Describing our solutions as spacetimes that satisfy Einstein's equations, we find that the relational dynamical system predicts two singular solutions of GR that are connected at the hypersurface of the singularity such that relational DOFs are continuous and the orientation of the spatial frame is inverted.

• The paper demonstrates that relational variables enable a deterministic, continuous description of cosmological evolution through big bang/crunch singularities.
• It contrasts chaotic vacuum dynamics with smooth, quiescent evolution within the Bianchi IX model to highlight key differences in behavior.
• The study lays a theoretical foundation for extending relational dynamics to complex gravitational systems and bridging relativistic and quantum theories.

Relationalism in Cosmological Evolution: Investigating the Bianchi IX Model and Singularities

The study presented by Koslowski, Mercati, and Sloan explores the application of relational principles to the dynamics of classical Bianchi IX cosmologies. By focusing on dimensionless ratios, the paper challenges traditional views on singularities within the framework of General Relativity (GR).

Core Concepts and Approach

Relationalism, which posits that only dimensionless ratios or relational degrees of freedom (DOFs) are physically meaningful, underpins this research. This perspective is rooted in the impossibility of defining absolute scales of time and distance within the universe itself, as measurements are inherently relational. The authors apply relationalism to classical Bianchi IX cosmology, dissolved from volume and expansion degrees of freedom.

The paper divides its focus into two main cosmological models: vacuum-dominated and quiescent Bianchi IX cosmologies. In the context of the vacuum-dominated model, the system is shown to exhibit chaotic dynamics with relational DOFs experiencing infinite changes, supporting the characteristic chaotic nature of Bianchi IX cosmologies. Meanwhile, the quiescent model illustrates how the universe can evolve through a big bang/crunch singularity by utilizing relational DOFs. Contrary to conventional descriptions, this singularity is not a termination point but a regular condition in the relational framework.

Numerical Findings and Predictions

A pivotal aspect of this work is the assertion that relational variables offer a deterministic and continuous description through singular points traditionally described as big bang/crunch events. The implications of these findings suggest that the singularities typical in GR do not undercut the continuity of physical law when described using relational variables.

The investigation unveils that near-singularity behavior in quiescent Bianchi IX cosmology aligns with a regular, smooth trajectory on the shape space, connecting two halves of a cosmology with inverted orientations. These insights suggest that potential consequences arise for discrete symmetries and may influence ongoing discussions regarding matter/antimatter asymmetry in particle physics.

Theoretical and Practical Implications

From a theoretical standpoint, the research extends the relational dynamic system beyond apparent singularities, providing a complete and consistent extension of classical physics through points that GR traditionally considers endpoints of evolution. This finding underscores the potential for relational variables to fundamentally alter our understanding of cosmological phenomena and the nature of spacetime at extreme conditions.

The results achieved in the homogeneous cosmology model set a precedent for further exploration in inhomogeneous settings. The mathematical foundations laid by this paper indicate that relational variables maintain their predictability and continuity even in complex gravitational systems.

Future Directions

The study prompts further investigation into how relational variables might be applied to other cosmological models, including more comprehensive inhomogeneous systems beyond homogeneous Bianchi IX models. Additionally, exploring the intersection of quantum effects and relational dynamics could yield significant advancements in bridging relativistic and quantum theories.

Overall, this paper provides critical insights into how relationalism can redefine our understanding of the universe's evolution, offering a novel and potentially transformative angle from which to approach longstanding challenges in cosmology and GR. Researchers in the field are encouraged to explore the robustness and limitations of the relational description across broader contexts and varying cosmological scenarios.