Kinetically Coupled Dark Matter Condensates

Dark matter consisting of ultralight bosons can form a macroscopic Bose-Einstein condensate with distinctive observational signatures. While this possibility has been extensively studied for axions and axion-like particles $-$ pseudoscalars with masses protected by shift symmetry $-$ realistic models from string theory and other higher-dimensional theories predict more complex structures. Here we investigate a two-field generalization where an axion couples to a moduli field through its kinetic term, representing the phase and radial modes of a complex scalar field. We demonstrate that when this system forms a gravitationally bound Bose-Einstein condensate, the kinetic coupling produces dramatic modifications to cosmological evolution compared to the canonical single-field case. Most notably, the axion Jeans scale becomes dynamically dependent on the moduli field's evolution, fundamentally altering structure formation. By mapping existing observational constraints from canonical axion models to our two-field scenario, we identify regions of parameter space that are already excluded by current observations. In particular, consistency with observations requires that the moduli field must take on small field values, $\chi/M_{\rm pl} \ll 1$, throughout most of cosmic history for this class of axions to remain a viable description of all dark matter.