Axion dark matter in a $3-3-1$ model

Slightly extending a right-handed neutrino version of the $3-3-1$ model, we show that it is not only possible to solve the strong CP problem but also to give the total dark matter abundance reported by the Planck collaboration. Specifically, we consider the possibility of introducing a $3-3-1$ scalar singlet to implement a gravity stable Peccei-Quinn mechanism in this model. Remarkably, for allowed regions of the parameter space, the arising axions with masses $m_a\approx$ meV can both make up the total dark matter relic density through non-thermal production mechanisms and be very close to the region to be explored by the IAXO helioscope.