Scalar field dark matter likely is able to solve the small-scale cosmology problems facing the cold dark matter ( CDM ) , and has become an emerging contender to challenge the CDM .
It however requires a particle mass \sim 1 - 2 \times 10 ^ { -22 } eV .
We find such an extremely small particle mass can naturally arise from a non-QCD axion mechanism , under fairly general assumptions that the axion is the dominant dark matter , and a few species of self-interacting light particles of comparable masses and a massless gauge boson both decouple from the bright sector since the photon temperature exceeds 200 GeV .
These assumptions also set the axion decay constant scale to several \times 10 ^ { 16 } GeV .
Given the above axion mass , we further pin down the dark-sector particles to consist of single-handed fermion and anti-fermion .
With a mass around 92 - 128 eV , these dark-sector fermions may constitute a minority population of dark matter .
In the simplest SU ( 2 ) gauge field model , a dilute instanton gas as dark photons can contribute to about 2.5 \% of the total relativistic relics in the cosmic microwave background radiation .