Asymptotic Theorems and Averaging in Scalar Field Cosmology
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| author | Leon, Genly Kozak, Aleksander Michea, Claudio |
| author_facet | Leon, Genly Kozak, Aleksander Michea, Claudio |
| contents | We present a hybrid study that combines a concise review of scalar-field cosmology with new analytic developments that integrate averaging reductions for oscillatory regimes with dynamical-systems techniques. For oscillatory fields, we derive an averaging reduction that yields an effective slow system whose time averages control dissipation; introducing uniform derivative bounds, Barbalat/LaSalle arguments, and a finite-dimensional center/stable manifold reduction, we carry out late-time analysis of the models. We prove persistence of equilibria, decay estimates, and local invariant manifolds under small $C^k$ perturbations of $χ(ϕ)$ and $G(a)$, quantify how averaged dissipation lifts to the full oscillatory dynamics with an $\mathcal{O}(H)$ error, and provide numerical examples. In addition to asymptotic reductions, we obtain exact quadrature solutions in general relativistic, anisotropic, and brane-world settings, yielding closed-form expressions for $t(a)$, $ϕ(a)$, and $H(a)$ and enabling analytic computation of inflationary observables. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_11987 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Asymptotic Theorems and Averaging in Scalar Field Cosmology Leon, Genly Kozak, Aleksander Michea, Claudio General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Mathematical Physics We present a hybrid study that combines a concise review of scalar-field cosmology with new analytic developments that integrate averaging reductions for oscillatory regimes with dynamical-systems techniques. For oscillatory fields, we derive an averaging reduction that yields an effective slow system whose time averages control dissipation; introducing uniform derivative bounds, Barbalat/LaSalle arguments, and a finite-dimensional center/stable manifold reduction, we carry out late-time analysis of the models. We prove persistence of equilibria, decay estimates, and local invariant manifolds under small $C^k$ perturbations of $χ(ϕ)$ and $G(a)$, quantify how averaged dissipation lifts to the full oscillatory dynamics with an $\mathcal{O}(H)$ error, and provide numerical examples. In addition to asymptotic reductions, we obtain exact quadrature solutions in general relativistic, anisotropic, and brane-world settings, yielding closed-form expressions for $t(a)$, $ϕ(a)$, and $H(a)$ and enabling analytic computation of inflationary observables. |
| title | Asymptotic Theorems and Averaging in Scalar Field Cosmology |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Mathematical Physics |
| url | https://arxiv.org/abs/2604.11987 |