  Constraints on the cosmic history of self-interacting Bose-Einstein condensed
(SIBEC) dark matter (DM) are obtained using the cosmic microwave background
(CMB), baryonic acoustic oscillations (BAO), growth factor measurements, and
type Ia supernovae (SNIa) distances. Four scenarios are considered, one with
purely SIBEC-DM, and three in which SIBEC-DM is the final product of some
transition from different initial states, which are either cold, warm, or has a
constant equation of state. Using a fluid approximation for the
self-interacting scalar field it is found that in the simplest scenario of
purely SIBEC-DM the self-interaction necessary for solving the cusp-core
problem, with core-radii of low-mass halos of order $R_c\gtrsim 1\text{kpc}$,
is excluded at $2.4\sigma$, or $98.5\%$ confidence. Introducing a transition,
however, relaxes this constraint, but the transitions are preferred to be after
matter-radiation equality, and the initial phase to be cold.
