  A light singlet scalar field feebly coupled through the super-renormalizable
Higgs portal provides a minimal and well-motivated realization of ultra-light
bosonic dark matter. We study the cosmological production of dark matter in
this model by elucidating the dynamics of two sources of scalar field
misalignment generated during the radiation era. For large scalar masses (above
order $10^{-3}\,{\rm eV}$), dark matter is produced through thermal
misalignment, by which the scalar field is driven towards large field values as
a result of the finite-temperature effective potential. The dominance of
thermal misalignment in this mass range leads to a sharp relic abundance
prediction which is, to a significant extent, insensitive to the initial
conditions of the scalar field. On the other hand, for low mass scalars (below
order $10^{-5}\,{\rm eV}$), dark matter is produced via VEV misalignment, which
is caused by the induced scalar field vacuum expectation value triggered by the
electroweak phase transition. We show that the relic abundance in this low mass
range is sensitive to the scalar field initial conditions. In the intermediate
mass range, the relic abundance is a consequence of a competition between
thermal misalignment and VEV misalignment, leading to novel forced resonance
effects which cause a recurring enhancement and suppression in the late time
oscillation amplitude as a function of the scalar mass. We compare our relic
abundance predictions with constraints and projections from equivalence
principle and inverse square law tests, stellar cooling, resonant molecular
absorption, and observations of extra-galactic background light and diffuse
X-ray backgrounds. New experimental ideas are needed to probe most of the
cosmologically motivated regions of parameter space.
