  The cold dark matter (CDM) scenario has proved successful in cosmology.
However, we lack a fundamental understanding of its microscopic nature.
Moreover, the apparent disagreement between CDM predictions and
subgalactic-structure observations has prompted the debate about its behaviour
at small scales. These problems could be alleviated if the dark matter is
composed of ultralight fields $m \sim 10^{-22}\ \text{eV}$, usually known as
fuzzy dark matter (FDM). Some specific models, with axion-like potentials, have
been thoroughly studied and are collectively referred to as ultralight axions
(ULAs) or axion-like particles (ALPs). In this work we consider anharmonic
corrections to the mass term coming from a repulsive quartic self-interaction.
Whenever this anharmonic term dominates, the field behaves as radiation instead
of cold matter, modifying the time of matter-radiation equality. Additionally,
even for high masses, i.e. masses that reproduce the cold matter behaviour, the
presence of anharmonic terms introduce a cut-off in the matter power spectrum
through its contribution to the sound speed. We analyze the model and derive
constraints using a modified version of CLASS and comparing with CMB and
large-scale structure data.
