  The core-cusp problem is a widely cited motivation for the exploration of
dark matter models beyond standard CDM. One such alternative is ULDM; extremely
light scalar particles exhibiting wavelike properties on kiloparsec scales.
Astrophysically realistic ULDM halos are expected to consist of inner solitonic
cores embedded in NFW-like outer halos. The presence of the solitonic core
suggests that ULDM may resolve the core-cusp discrepancy associated with pure
NFW halos without recourse to baryonic physics. However, it has been
demonstrated that the density of ULDM halos can exceed those of comparable NFW
configurations at some radii and halo masses, apparently exacerbating the
problem rather than solving it. This situation arises because, although
solitonic cores are flat at their centres, they obey an inverse mass-radius
scaling relationship. Meanwhile, the mass of the inner soliton increases with
the total halo mass, and therefore the inner core becomes more peaked at large
halo masses. We describe a parameterisation of the radial density profiles of
ULDM halos that allows for environmental variability of the core-halo mass
relation in order to investigate this issue in more detail. For halos up to
10^12 solar masses we find feasible ULDM profiles for which the central density
is lower than their NFW counterparts at astrophysically accessible radii.
However, comparisons to observed profiles do not strongly favour either option;
both give reasonable fits to subsets of the data for some parameter choices.
Consequently, we find that robust tests of the core-cusp problem in ULDM will
require more comprehensive observational data and simulations that include
baryonic feedback.
