Controlled Penumbral Inflation from Monodromic Valleys

TL;DR

This paper identifies conditions under which long monodromic valleys in complex-structure moduli space support controlled inflation, introducing a minimal exactly solvable model that advances the predictive power of penumbral inflation scenarios.

Contribution

It demonstrates how local branch data determine controlled inflation support in monodromic valleys and provides the first exactly solvable penumbral inflation model.

Findings

A branch-displacing odd term creates a plateau when Δ>0.

Covariant single-clock control requires p<2 or p=2 with large parameters.

A minimal analytic family with a closed-form valley is constructed.

Abstract

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 $\Delta\equiv p+2\nu-q>0$, 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.