Ultralight DM bosons with an axion-like potential: scale-dependent constraints revisited

A scalar field ? endowed with a trigonometric potential has been proposed to play the role of Dark Matter. deep study cosmological evolution linear perturbations, and its comparison Cold Matter (CDM) Fuzzy (FDM) cases (scalar quadratic potential), reveals an enhancement in amplitude mass power spectrum for large wave numbers due non-linearity axion-like potential. For first time, we scale-dependence on physical quantities such as growth factor Dk, velocity fk, fk ?8. We found that z<10, all these recover CDM evolution, whereas high redshift there is clear distinction between each model (FDM case, potential) depending wavenumber k decay parameter well. semi-analytical Halo Mass Function also revisited, finding suppression number low halos, FDM but small increment variance halo function Finally, present constraints axion by using data Planck Collaboration 2018 Lyman-? forest.