  We show that the present dark matter abundance can be accounted for by an
oscillating scalar field that acquires both mass and a non-zero expectation
value from interactions with the Higgs field. The dark matter scalar field can
be sufficiently heavy during inflation, due to a non-minimal coupling to
gravity, so as to avoid the generation of large isocurvature modes in the CMB
anisotropies spectrum. The field begins oscillating after reheating, behaving
as radiation until the electroweak phase transition and afterwards as
non-relativistic matter. The scalar field becomes unstable, although
sufficiently long-lived to account for dark matter, due to mass mixing with the
Higgs boson, decaying mainly into photon pairs for masses below the MeV scale.
In particular, for a mass of $\sim 7$ keV, which is effectively the only free
parameter, the model predicts a dark matter lifetime compatible with the recent
galactic and extragalactic observations of a 3.5 keV X-ray line.
