Dynamics of the Bianchi~V cosmological model inspired by quintessential $α$-attractors
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| Format: | Preprint |
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2026
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| _version_ | 1866908848849158144 |
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| author | Leon, Genly Abebe, Amare Paliathanasis, Andronikos |
| author_facet | Leon, Genly Abebe, Amare Paliathanasis, Andronikos |
| contents | We investigate scalar-field cosmologies in the Bianchi V spacetime using a dynamical-systems framework. Motivated by representative $α$-attractor potentials - the E-model and T-model - we apply averaging theorems and amplitude--phase reductions to monomial potentials $\sim ϕ^{2n}$ of the scalar field, which approximate the attractor models near their minima, in the presence of matter with barotropic index $γ$. The reduced averaged system admits five generic isolated equilibria: Kasner vacua $\mathcal{K}_0^\pm$, the matter FLRW point $\mathcal{F}$, the scalar FLRW point $\mathcal{S}$, and the curvature Milne-type point $\mathcal{K}$, together with special families for tuned $(n,γ)$. We find that $\mathcal{K}_0^\pm$ are always sources, $\mathcal{F}$ is generically a saddle but can act as a sink for $γ<\min\{\tfrac{2n}{n+1},\tfrac{2}{3}\}$, $\mathcal{S}$ is a sink if $0<n<\tfrac{1}{2}$ and $\tfrac{2n}{n+1}<γ\leq 2$, while $\mathcal{K}$ becomes a sink whenever $γ>\tfrac{2}{3}$ and $n>\tfrac{1}{2}$. These results demonstrate that isotropic FLRW $α$-attractor models extend naturally to anisotropic Bianchi~V cosmologies: inflationary attractors remain robust, while the Milne-type curvature solution emerges as the late-time state. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_20072 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Dynamics of the Bianchi~V cosmological model inspired by quintessential $α$-attractors Leon, Genly Abebe, Amare Paliathanasis, Andronikos General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics We investigate scalar-field cosmologies in the Bianchi V spacetime using a dynamical-systems framework. Motivated by representative $α$-attractor potentials - the E-model and T-model - we apply averaging theorems and amplitude--phase reductions to monomial potentials $\sim ϕ^{2n}$ of the scalar field, which approximate the attractor models near their minima, in the presence of matter with barotropic index $γ$. The reduced averaged system admits five generic isolated equilibria: Kasner vacua $\mathcal{K}_0^\pm$, the matter FLRW point $\mathcal{F}$, the scalar FLRW point $\mathcal{S}$, and the curvature Milne-type point $\mathcal{K}$, together with special families for tuned $(n,γ)$. We find that $\mathcal{K}_0^\pm$ are always sources, $\mathcal{F}$ is generically a saddle but can act as a sink for $γ<\min\{\tfrac{2n}{n+1},\tfrac{2}{3}\}$, $\mathcal{S}$ is a sink if $0<n<\tfrac{1}{2}$ and $\tfrac{2n}{n+1}<γ\leq 2$, while $\mathcal{K}$ becomes a sink whenever $γ>\tfrac{2}{3}$ and $n>\tfrac{1}{2}$. These results demonstrate that isotropic FLRW $α$-attractor models extend naturally to anisotropic Bianchi~V cosmologies: inflationary attractors remain robust, while the Milne-type curvature solution emerges as the late-time state. |
| title | Dynamics of the Bianchi~V cosmological model inspired by quintessential $α$-attractors |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2602.20072 |