Cosmic acceleration as a saddle-node bifurcation: background identities and structure
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917212374171648 |
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| author | Cotsakis, Spiros |
| author_facet | Cotsakis, Spiros |
| contents | We show that the late-time acceleration of the universe can be understood as a codimension-one bifurcation of the Friedmann dynamical system in the variables $(H,Ω)$. At a critical value of the density-parameter combination, a saddle-node bifurcation occurs; beyond the saddle-node, trajectories are globally attracted to a new accelerating fixed point. We obtain a normal form and a versal unfolding for the reduced dynamics, proving robustness (structural stability) of the phenomenon and deriving the characteristic square-root splitting of the emerging equilibria. We interpret the unfolding parameter as a measure of departure from adiabaticity via a modified continuity/entropy balance, thus linking acceleration to controlled non-equilibrium evolution rather than to a cosmological constant. In particular, late-time acceleration arises without invoking a separate dark-energy fluid; it emerges from a bounded unfolding of the background flow around a saddle-node organizing center. We situate this within a broader "general-relativity landscape," where control parameters act as moduli and branches of exact solutions appear as equilibrium loci, allowing bifurcation-theoretic tools to organize cosmological dynamics without introducing extra fields, and suggesting a coherent, bifurcation-guided cosmic history. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_20430 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cosmic acceleration as a saddle-node bifurcation: background identities and structure Cotsakis, Spiros General Relativity and Quantum Cosmology We show that the late-time acceleration of the universe can be understood as a codimension-one bifurcation of the Friedmann dynamical system in the variables $(H,Ω)$. At a critical value of the density-parameter combination, a saddle-node bifurcation occurs; beyond the saddle-node, trajectories are globally attracted to a new accelerating fixed point. We obtain a normal form and a versal unfolding for the reduced dynamics, proving robustness (structural stability) of the phenomenon and deriving the characteristic square-root splitting of the emerging equilibria. We interpret the unfolding parameter as a measure of departure from adiabaticity via a modified continuity/entropy balance, thus linking acceleration to controlled non-equilibrium evolution rather than to a cosmological constant. In particular, late-time acceleration arises without invoking a separate dark-energy fluid; it emerges from a bounded unfolding of the background flow around a saddle-node organizing center. We situate this within a broader "general-relativity landscape," where control parameters act as moduli and branches of exact solutions appear as equilibrium loci, allowing bifurcation-theoretic tools to organize cosmological dynamics without introducing extra fields, and suggesting a coherent, bifurcation-guided cosmic history. |
| title | Cosmic acceleration as a saddle-node bifurcation: background identities and structure |
| topic | General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2502.20430 |