Mode interactions in scalar field cosmology
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arXiv
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| Format: | Preprint |
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2025
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| author | Cotsakis, Spiros Antoniadis, Ignatios |
| author_facet | Cotsakis, Spiros Antoniadis, Ignatios |
| contents | We study the dynamics of spatially homogeneous Friedmann--Robertson--Walker universes filled with a massive scalar field in a neighbourhood of the massless transition $s=1$. At this point the Einstein--scalar system exhibits a codimension--two Hopf--steady--state organising centre whose versal unfolding describes all small deformations of the quadratic model. After reduction to the centre manifold, the dynamics is governed by two slow geometric modes $(r,z)$: the Hopf amplitude $r$, measuring the kinetic departure from de Sitter, and the slowly drifting Hubble mode $z$. We show that the standard slow--roll parameters follow directly from these unfolding variables, $ε\sim\tfrac32 r^{2}$ and $η\sim z$, so that the spectral tilt, tensor--to--scalar ratio, and scalar amplitude arise as universal functions of $(r,z)$, independently of the choice of potential. The two unfolding parameters $(μ_{1},μ_{2})$ classify all perturbations of the quadratic model and can be interpreted physically as controlling the tilt and curvature deformations of generic polynomial inflationary potentials. Thus the near scale--invariance of primordial perturbations emerges as a structural property of the unfolding of the organising centre, providing a potential--independent mechanism for an early phase of accelerated expansion. We discuss the implications of this geometric framework for the interpretation and classification of inflationary models. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_04607 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Mode interactions in scalar field cosmology Cotsakis, Spiros Antoniadis, Ignatios General Relativity and Quantum Cosmology High Energy Physics - Theory We study the dynamics of spatially homogeneous Friedmann--Robertson--Walker universes filled with a massive scalar field in a neighbourhood of the massless transition $s=1$. At this point the Einstein--scalar system exhibits a codimension--two Hopf--steady--state organising centre whose versal unfolding describes all small deformations of the quadratic model. After reduction to the centre manifold, the dynamics is governed by two slow geometric modes $(r,z)$: the Hopf amplitude $r$, measuring the kinetic departure from de Sitter, and the slowly drifting Hubble mode $z$. We show that the standard slow--roll parameters follow directly from these unfolding variables, $ε\sim\tfrac32 r^{2}$ and $η\sim z$, so that the spectral tilt, tensor--to--scalar ratio, and scalar amplitude arise as universal functions of $(r,z)$, independently of the choice of potential. The two unfolding parameters $(μ_{1},μ_{2})$ classify all perturbations of the quadratic model and can be interpreted physically as controlling the tilt and curvature deformations of generic polynomial inflationary potentials. Thus the near scale--invariance of primordial perturbations emerges as a structural property of the unfolding of the organising centre, providing a potential--independent mechanism for an early phase of accelerated expansion. We discuss the implications of this geometric framework for the interpretation and classification of inflationary models. |
| title | Mode interactions in scalar field cosmology |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.04607 |