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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2605.10197 |
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| _version_ | 1866909031343325184 |
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| author | Pirzada Li, Tianjun |
| author_facet | Pirzada Li, Tianjun |
| contents | Long monodromic valleys arise in the penumbra of complex-structure moduli space. We show that their local branch data already determine whether they support controlled inflation, and thereby isolate the first controlled penumbral inflationary window. In the axion--saxion effective theory given in Eq.4, a branch-displacing odd term generates a plateau when $Δ\equiv p+2ν-q>0$, while covariant single-clock control further requires $p<2$, or $p=2$ with $12A_pm^2/V_0\gg1$ over the observational window. This splits penumbral valleys into no plateau, uncontrolled plateau, and controlled plateau before global completion is attempted. We identify a minimal analytic family with a closed-form valley and an invariant attractor equation for the full two-field dynamics, providing the first exactly solvable penumbral realization that remains predictive under the next penumbral order. The penumbra is thus promoted from a geometric suggestion to a predictive search principle. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10197 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Controlled Penumbral Inflation from Monodromic Valleys Pirzada Li, Tianjun High Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology Long monodromic valleys arise in the penumbra of complex-structure moduli space. We show that their local branch data already determine whether they support controlled inflation, and thereby isolate the first controlled penumbral inflationary window. In the axion--saxion effective theory given in Eq.4, a branch-displacing odd term generates a plateau when $Δ\equiv p+2ν-q>0$, while covariant single-clock control further requires $p<2$, or $p=2$ with $12A_pm^2/V_0\gg1$ over the observational window. This splits penumbral valleys into no plateau, uncontrolled plateau, and controlled plateau before global completion is attempted. We identify a minimal analytic family with a closed-form valley and an invariant attractor equation for the full two-field dynamics, providing the first exactly solvable penumbral realization that remains predictive under the next penumbral order. The penumbra is thus promoted from a geometric suggestion to a predictive search principle. |
| title | Controlled Penumbral Inflation from Monodromic Valleys |
| topic | High Energy Physics - Phenomenology Cosmology and Nongalactic Astrophysics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2605.10197 |