Constraining Ultra-light Axions with Galaxy Cluster Number Counts
  In this paper we investigate the potential of current and upcoming
cosmological surveys to constrain the mass and abundance of ultra-light axion
(ULA) cosmologies with galaxy cluster number counts. ULAs, sometimes also
referred to as Fuzzy Dark Matter, are well-motivated in many theories beyond
the Standard Model and could potentially solve the $\Lambda$CDM small-scale
crisis. Galaxy cluster counts provide a robust probe of the formation of
structures in the Universe. Their distribution in mass and redshift is strongly
sensitive to the underlying linear matter perturbations. In this forecast paper
we explore two scenarios, firstly an exclusion limit on axion mass given a
no-axion model and secondly constraints on an axion model. With this we obtain
lower limits on the ULA mass on the order of $m_a \gtrsim 10^{-24}$ eV.
However, this result depends heavily on the mass of the smallest reliably
observable clusters for a given survey. Cluster counts, like many other
cosmological probes, display an approximate degeneracy in the ULA mass vs.
abundance parameter space, which is dependent on the characteristics of the
probe. These degeneracies are different for other cosmological probes. Hence
galaxy cluster counts might provide a complementary window on the properties of
ultra-light axions.
