  Dark matter (DM) and neutrinos are the two most compelling pieces of evidence
of new physics beyond the Standard Model of Particle Physics but these are
often treated as belonging to two different sectors. Yet DM-neutrino
interactions are known to have cosmological consequences. Here, we study the
scenario of a scalar DM candidate coupled to left-handed neutrinos via a Dirac
mediator. We determine the mass of a DM candidate that yields the right DM
relic abundance in a thermal scenario and it is consistent with large-scale
structure formation. In order to satisfy both constraints, a complex DM
candidate should have a mass larger than $8.14$ keV while the mass of a real DM
candidate should be above $18.1$ eV, independently of the value of the
DM-neutrino coupling.
