Spinor driven cosmic bounces and their cosmological perturbations
Open accessAbstract
When coupling fermions to gravity, torsion is naturally induced. We consider the possibility that fermion bilinears can act as a source for torsion, altering the dynamics of the early universe such that the big bang gets replaced with a classical nonsingular bounce. We extend previous studies in several ways: we allow more general fermion couplings, consider both commuting and anticommuting spinors, and demonstrate that with an appropriate choice of potential one can easily obtain essentially arbitrary equations of state, including violations of the null energy condition, as required for a bounce. As an example, we construct a model of ekpyrotic contraction followed by a nonsingular bounce into an expanding phase. We analyze cosmological fluctuations in these models, and show that the perturbations can be rewritten in real fluid form. We find indications that spinor bounces are stable, and exhibit several solutions for the perturbations. Interestingly, spinor models do not admit a scalar-vector-tensor decomposition, and consequently some types of scalar fluctuations can act as a source for gravitational waves already at linear order. We also find that the first order dynamics are directionally dependent, an effect which might lead to distinguished observational signatures.
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At the background level the bounce is a nonsingular ρ2-type bounce, similar in spirit to the effective Friedmann equation in loop quantum cosmology and to other torsion-based bouncing models.
“At the background level this is a nonsingular ρ 2 -type bounce, similar in spirit to the effective Friedmann equation in loop quantum cosmology [35] and to other torsion-based bouncing models [22,29].”
From Dynamical systems analysis of an Einstein–Cartan ekpyrotic nonsingular bounce cosmology (2026) · cites this paper as [22]
Most of these papers focus on the spin-sector microphysics and on particular background or perturbative solutions; for example, Ref. [22] studies exact spinor-driven ekpyrotic bounce backgrounds and their perturbations, rather than the global phase-space structure of a scalar-fluid-spin system in a dynamical-systems picture.
“As noted above, most of these papers focus on the spin-sector microphysics and on particular background or perturbative solutions.For example, Ref. [22] studies exact spinordriven ekpyrotic bounce backgrounds and their perturbations, rather than the global phase-space structure of a scalar-fluid-spin system in a dynamical-systems pic-ture.”
From Dynamical systems analysis of an Einstein–Cartan ekpyrotic nonsingular bounce cosmology (2026) · cites this paper as [22]
Farnsworth, Lehners, and Qiu constructed a single-field Einstein-Cartan model in which a spinor condensate drives both ekpyrotic contraction and a torsion-induced bounce, and analyzed the associated cosmological perturbations in detail.
“In particular, Farnsworth, Lehners, and Qiu constructed a singlefield Einstein-Cartan model in which a spinor condensate drives both ekpyrotic contraction and a torsion-induced bounce, and analyzed the associated cosmological perturbations in detail [22].”
From Dynamical systems analysis of an Einstein–Cartan ekpyrotic nonsingular bounce cosmology (2026) · cites this paper as [22]
Torsion-induced bounces have been realized in Einstein-Cartan and related torsionful models, including spinor-based constructions in which a single Dirac field drives both ekpyrotic contraction and a torsion-supported bounce.
“Torsion-induced bounces have also been realized in Einstein-Cartan and related torsionful models, including spinor-based constructions in which a single Dirac field drives both ekpyrotic contraction and a torsionsupported bounce [11-13, 22, 28, 29].”
From Dynamical systems analysis of an Einstein–Cartan ekpyrotic nonsingular bounce cosmology (2026) · cites this paper as [22]
The construction is complementary to microphysics-focused ECSK spinor models and to spinor-driven ekpyrotic bounce scenarios such as Ref. [22]: the emphasis is on global phase-space structure of a two-component (scalar + spin fluid) system, mapping fixed points, basins of attraction, and Lyapunov stability, while treating parameters such as the Weyssenhoff coefficient α and the softening scale as
“In this way the construction is complementary to microphysics-focused ECSK spinor models and to spinor-driven ekpyrotic bounce scenarios such as Ref. [22]: the emphasis here is on the global phase-space structure of a two-component (scalar + spin fluid) system, mapping fixed points, basins of attraction, and Lyapunov stability, while treating parameters such as the Weyssenhoff coefficient α and”
From Dynamical systems analysis of an Einstein–Cartan ekpyrotic nonsingular bounce cosmology (2026) · cites this paper as [22]
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Cites
Towards a nonsingular bouncing cosmology
Cai, Y.-F., Easson, D. A., & Brandenberger, R. (2012) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2012/08/020 · Cited by 439 · see citing works
Ekpyrotic and Cyclic Cosmology
Lehners, J.-L. (2008) · Physics Reports · doi:10.1016/j.physrep.2008.06.001 · Cited by 381 · see citing works
Self-citationNonsingular, big-bounce cosmology from spinor-torsion coupling
Popławski, N. (2012) · Physical Review D · doi:10.1103/physrevd.85.107502 · Cited by 180 · see citing works
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Dynamical systems analysis of an Einstein–Cartan ekpyrotic nonsingular bounce cosmology
Stingley, J. (2026) · General Relativity and Gravitation · doi:10.1007/s10714-026-03547-w
- Authors
- Farnsworth, S., Lehners, J.-L., & Qiu, T.
- Affiliations
- Max Planck Institute for Gravitational Physics (DE)
- Central China Normal University (CN)
- Venue
- Physical Review D
- Publisher
- American Physical Society (APS)
- Published
- 2017-10-30
- Volume
- 96
- Issue
- 8
- ISSN
- 2470-0010 (ISSN-L)
- 2470-0029
- OpenAlex
- W2756261334
- Cited by
- 16
- References
- 3
- Citations by year
- 2026: 2 · 2025: 1 · 2024: 2 · 2021: 1 · 2020: 3 · 2019: 4 · 2018: 3
- FWCI
- 1.50
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. D/Physical review. D. (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Max Planck Digital Library (submittedVersion, other-oa)
- MPG.PuRe (Max Planck Society) (submittedVersion, other-oa)
- arXiv (Cornell University)
- Funders
- National Natural Science Foundation of China (11405069, 11653002)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Noncommutative and Quantum Gravity Theories
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
- Keywords
- non-singular bounce, torsion, fermion bilinears, cosmological perturbations, null energy condition violation, gravitational waves, early universe cosmology
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