Heavy particles are not the only interpretation for the observed coldness of dark matter - here I present cosmological simulations of a cold Bose-Einstein state, revealing an unknown world of non-linear wave structures that distinguish this physically well motivated state from standard particle CDM. The key predictions are made with GPU optimised AMR evolution of coupled Schrodinger-Poisson equations, finding solitonic cores and a granular structure within virialised halos. Comparison with the latest Hubble Frontier Field galaxies that we have detected at high redshift favours this interpretation, as do the large cores derived for dwarf galaxies and by QSO flux anomalies. This exploration is timely because of the continued laboratory absence of WIMPs, and may establish light bosons as the most viable interpretation of dark matter.