Nonsingular, Big-Bounce Cosmology from Spinor-Torsion Coupling
The paper by Nikodem Popławski presents a novel cosmological model by extending the framework of the Einstein-Cartan-Sciama-Kibble (ECSK) theory of gravity. The ECSK theory allows for a non-symmetric affine connection, where the torsion tensor, a measure of this asymmetry, acts as a dynamical variable. In this framework, the torsion becomes significant in fermionic matter at extremely high densities, which was posited to occur in the early universe.
The central outcome of this paper is the proposal that the minimal coupling of the torsion tensor with Dirac spinors, such as in the case of fermionic matter, induces a spin-spin interaction. This interaction counters the singularity predicted by general relativity (GR) in the form of the Big Bang, instead suggesting a nonsingular, "big-bounce" cosmology. The universe undergoes a contraction phase until it reaches a minimum scale factor, at which point the spin-induced repulsion causes it to bounce and transition into an expansion phase. The conditions leading to this bounce are marked by extremely high densities, estimated around the Planck density, beyond which conventional GR collapses into a singularity.
Key Results
- Spin-spin Interaction and Avoidance of Singularity: The torsion-induced spin-spin interaction introduces a form of gravitational repulsion at very high densities, circumventing the Big Bang singularity by causing a "bounce" at a minimum, non-zero scale factor.
- Implications for Homogeneity and Isotropy: Due to the spinor-torsion interactions, the universe post-bounce evolves in such a way that it appears spatially flat, homogeneous, and isotropic on large scales, addressing classical cosmological issues such as horizon and flatness problems without invoking inflation.
- Analytical Predictions for Scale Factor and Cosmic Time: By utilizing the Friedman-Lemaître-Robertson-Walker (FLRW) metric and deriving the associated equations of motion, the paper provides expressions relating the scale factor to cosmic temperature and time. It predicts a critical temperature and scale factor below which the universe bounces, rather than contracting to a singularity.
Implications and Future Work
These findings deepen our understanding of the potential role of torsion in gravity and its implications for early universe cosmology. The avoidance of singularities through torsion could present an alternative to inflationary models, potentially leading to novel routes in resolving long-standing issues in cosmology without introducing new scalar fields or dark energy components. Furthermore, these models might offer testable predictions through their effects on cosmic microwave background radiation or large-scale structure, warranting future investigation.
Given the unique coupling features of spinors and torsion, further work could explore extensions of this model to other forms of matter, including non-standard spins or effectively testing its predictions against astrophysical observations. Additionally, the integration of these results with quantum field theory or quantum gravity approaches may provide a more comprehensive theory for describing early universe physics.
In summary, Popławski's work introduces meaningful modification to the standard cosmological model by leveraging the ECSK framework. It presents a compelling case for reconsidering the role of torsion in a high-density regime, potentially guiding future theoretical developments and observational tests in cosmology.