  We investigate cosmological structure formation in Fuzzy Dark Matter (FDM)
with an attractive self-interaction (SI) with numerical simulations. Such a SI
would arise if the FDM boson were an ultra-light axion, which has a strong CP
symmetry-breaking scale (decay constant). Although weak, the attractive SI may
be strong enough to counteract the quantum 'pressure' and alter structure
formation. We find in our simulations that the SI can enhance small-scale
structure formation, and soliton cores above a critical mass undergo a phase
transition, transforming from dilute to dense solitons.
