Dark matter from an ultra-light pseudo-Goldsone-boson

Dark matter (DM) and dark energy (DE) can be both described in terms of ultra-light pseudo-Goldstone-bosons (PGB) with masses mDM≳10−23eV and mDE≲10−33eV respectively. Following Barbieri et al., we entertain the possibility that a PGB exists with mass mI intermediate between these two limits, giving a partial contribution to DM. We evaluate the related effects on the power spectrum of the matter density perturbations and on the cosmic microwave background and we derive the bounds on the density fraction, fI, of this intermediate field from current data, with room for a better sensitivity on fI in the near future. We also give a simple and unified analytic description of the free streaming effects both for an ultra-light scalar and for a massive neutrino.