  We consider the possibility of simultaneously addressing the dark matter
problem and neutrino mass generation in the minimal inverse seesaw realisation.
The Standard Model is extended by two right-handed neutrinos and three sterile
fermionic states, leading to three light active neutrino mass eigenstates, two
pairs of (heavy) pseudo-Dirac mass eigenstates and one (mostly) sterile state
with mass around the keV, possibly providing a dark matter candidate, and
accounting for the recently observed and still unidentified monochromatic 3.5
keV line in galaxy cluster spectra. The conventional production mechanism
through oscillation from active neutrinos can account only for $\sim 43\%$ of
the observed relic density. This can be slightly increased to $\sim 48\%$ when
including effects of entropy injection from the decay of light (with mass below
20 GeV) pseudo-Dirac neutrinos. The correct relic density can be achieved
through freeze-in from the decay of heavy (above the Higgs mass) pseudo-Dirac
neutrinos. This production is only effective for a limited range of masses,
such that the decay occurs not too far from the electroweak phase transition.
We thus propose a simple extension of the inverse seesaw framework, with an
extra scalar singlet coupling to both the Higgs and the sterile neutrinos,
which allows to achieve the correct dark matter abundance in a broader region
of the parameter space, in particular in the low mass region for the
pseudo-Dirac neutrinos.

High Energy Physics - Phenomenology;Cosmology and Nongalactic Astrophysics