Persistence and Transition Varieties in Scalar Field Cosmology
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arXiv
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2026
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| author | Cotsakis, Spiros |
| author_facet | Cotsakis, Spiros |
| contents | We develop a bifurcation-theoretic description of Friedmann--Robertson--Walker cosmologies with a scalar field $ϕ$, a barotropic fluid of index $γ$, and spatial curvature. For the strict exponential potential $V(ϕ)=V_{0}e^{λϕ}$, with $a=\sqrt{3/2}\,λ$, the local phase portrait is organised by five loci in the $(γ,a)$-plane: $|a|=3$, $a^{2}=3$, $a^{2}=9γ/2$, $γ=2/3$, and $γ=2$. Near these loci we compute translated jets, centre(-like) reductions, and normal forms governing persistence and transitions. For the quadratic potential $V(ϕ)=(1/2)m^{2}ϕ^{2}$, the effective slope $λ$ is dynamical. Using the bounded variable $ζ=\arctanλ$, we obtain a regular autonomous $4$-dimensional system in $(X,Y,Ω_{k},ζ)$, where $Ω_{k}$ is the curvature variable. This reveals invariant gates, robust equilibrium continua, and vertical $γ$-thresholds for loss and recovery of normal hyperbolicity. We then construct an explicit stratification for the exponential class and a pull-back stratification for the massive case, together with the corresponding physical path maps into unfolding space. The resulting framework also organises slow-roll, ultra slow-roll, and oscillatory regimes. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_05617 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Persistence and Transition Varieties in Scalar Field Cosmology Cotsakis, Spiros General Relativity and Quantum Cosmology Dynamical Systems We develop a bifurcation-theoretic description of Friedmann--Robertson--Walker cosmologies with a scalar field $ϕ$, a barotropic fluid of index $γ$, and spatial curvature. For the strict exponential potential $V(ϕ)=V_{0}e^{λϕ}$, with $a=\sqrt{3/2}\,λ$, the local phase portrait is organised by five loci in the $(γ,a)$-plane: $|a|=3$, $a^{2}=3$, $a^{2}=9γ/2$, $γ=2/3$, and $γ=2$. Near these loci we compute translated jets, centre(-like) reductions, and normal forms governing persistence and transitions. For the quadratic potential $V(ϕ)=(1/2)m^{2}ϕ^{2}$, the effective slope $λ$ is dynamical. Using the bounded variable $ζ=\arctanλ$, we obtain a regular autonomous $4$-dimensional system in $(X,Y,Ω_{k},ζ)$, where $Ω_{k}$ is the curvature variable. This reveals invariant gates, robust equilibrium continua, and vertical $γ$-thresholds for loss and recovery of normal hyperbolicity. We then construct an explicit stratification for the exponential class and a pull-back stratification for the massive case, together with the corresponding physical path maps into unfolding space. The resulting framework also organises slow-roll, ultra slow-roll, and oscillatory regimes. |
| title | Persistence and Transition Varieties in Scalar Field Cosmology |
| topic | General Relativity and Quantum Cosmology Dynamical Systems |
| url | https://arxiv.org/abs/2604.05617 |