Attractive (s)axions: cosmological trackers at the boundary of moduli space

We study the cosmological evolution of a FLRW universe dominated by the energy density of moduli close to asymptotic regions of moduli space. Due to the structure of the $\mathcal{N}=1$ SUGRA kinetic term, a saxion and an axion residing in the same chiral multiplet are (universally) coupled even if the latter is a flat direction of the potential, resulting in non-trivial dynamics. We generalise known results in the literature to the case of multiple moduli, showing the existence of various ``tracker" attractor solutions where the relative energy densities of many components (axions included) stay in a fixed ratio throughout the evolution. We conclude with some phenomenological applications, relevant for both the early and late universe.