Toward a Unified Axion Cosmology

Abstract: We explore a unified axion framework connecting grand unification, string-inspired axion-like particles (ALPs), and cosmology. Starting from the QCD axion associated with Peccei--Quinn symmetry in supersymmetric SO(10) GUT, we consider the broader spectrum of ultralight ALPs motivated by heterotic string theory. Within this multi-axion structure, we focus on two ultralight scales selected by cosmological requirements. A mode of order $10<sup>{-22}$ eV is assumed to constitute the dominant dark-matter component and can form a Bose--Einstein condensate whose attractive self-interaction leads to nonlinear collapse, providing possible seeds for high-redshift supermassive black holes. A lighter eigen-direction with a characteristic dynamical scale of order $10<sup>{-28}$ eV can transiently increase the pre-recombination expansion rate and reduce the sound horizon. An order-of-magnitude estimate shows that addressing the Hubble tension requires a sound-horizon-weighted axion fraction of order 0.1, corresponding, for a large initial displacement, to an effective decay constant of order $10<sup>{18}$ GeV. We show that a multi-axion--multi-instanton system can in principle provide both the required aligned light direction and a higher-order effective potential that makes the $10<sup>{-28}$ eV contribution transient. The framework links theoretically motivated axionic degrees of freedom to the distinct scales required by dark-matter, early-black-hole, and Hubble-tension phenomenology.