  Ultralight scalar dark matter with mass at or below the eV scale and pressure
from repulsive self-interaction could form a Bose-Einstein condensate in the
early Universe and maybe in galaxies as well. It has been suggested to be a
possible solution to the cusp/core problem or even to explain MOND
phenomenology. In this paper, I initiate a study of possible self-interactions
of ultralight scalar dark matter from the particle physics point of view. To
protect its mass, the scalar dark matter is identified as a pseudo
Nambu-Goldstone boson (pNGB). Quite a few pNGB models with different potentials
such as the QCD axion and the dilaton lead to attractive self-interactions. Yet
if an axion is a remnant of a 5D gauged U(1) symmetry, its self-interactions
could be repulsive provided the masses and charges of the 5D matter
contributing to its potential satisfy certain constraints. Collective symmetry
breaking could also lead to a repulsive self-interaction yet with too large a
strength that is ruled out by Bullet Cluster constraints. I also discuss
cosmological and astrophysical constraints on ultralight repulsive dark matter
in terms of a parametrization motivated by particle physics considerations.
