Axion production in axio-dilaton models outside the standard misalignment window

Determine a viable mechanism that produces the correct initial axion energy density in the axio-dilaton dark-sector cosmology when the axion decay constant f lies outside the parameter window where the standard vacuum misalignment mechanism typically applies, ensuring consistency with the derivative coupling W(chi) and the absence of direct axion–matter couplings assumed in the model.

Background

In the axio-dilaton dark-sector framework, the axion serves as Dark Matter through coherent oscillations around a quadratic minimum, with its effective mass and decay constant governed by the dilaton-dependent kinetic function W(chi). The standard vacuum misalignment mechanism relates the axion mass and decay constant f to the observed Dark Matter abundance, typically requiring f within a broad window (e.g., values around 10^4–10^15 GeV for conventional scenarios).

The paper argues that for extremely low values of f (as suggested by certain Yoga-inspired constructions), the usual misalignment production cannot apply, and UV physics or derivative interactions with a rolling dilaton could alter production. However, the authors explicitly leave the question of axion production unresolved for cases where f is outside the usual misalignment window.