Spinors, Inflation, and Non-Singular Cyclic Cosmologies

TL;DR

This paper explores cosmological models with spinor fields, revealing their potential to produce non-singular cyclic universes and analyzing their inflationary behavior, which differs from scalar field models.

Contribution

It introduces novel cosmological solutions involving spinor fields, including non-singular cyclic models, and assesses their inflationary dynamics and perturbation spectra.

Findings

Spinor-driven inflation yields a blue spectrum of density perturbations.

Non-singular cyclic cosmologies are possible with simple quartic spinor self-interactions.

Spinor fields can be approximated in certain quantum systems, offering new modeling approaches.

Abstract

We consider toy cosmological models in which a classical, homogeneous, spinor field provides a dominant or sub-dominant contribution to the energy-momentum tensor of a flat Friedmann-Robertson-Walker universe. We find that, if such a field were to exist, appropriate choices of the spinor self-interaction would generate a rich variety of behaviors, quite different from their widely studied scalar field counterparts. We first discuss solutions that incorporate a stage of cosmic inflation and estimate the primordial spectrum of density perturbations seeded during such a stage. Inflation driven by a spinor field turns out to be unappealing as it leads to a blue spectrum of perturbations and requires considerable fine-tuning of parameters. We next find that, for simple, quartic spinor self-interactions, non-singular cyclic cosmologies exist with reasonable parameter choices. These solutions might eventually be incorporated into a successful past- and future-eternal cosmological model free of singularities. In an Appendix, we discuss the classical treatment of spinors and argue that certain quantum systems might be approximated in terms of such fields.