Constraining cosmology with the velocity function of low-mass galaxies

The number density of field galaxies per rotation velocity, referred to as the velocity function, is an intriguing statistical measure probing the smallest scales of structure formation. In this paper we point out that the velocity function is sensitive to small shifts in key cosmological parameters such as the amplitude of primordial perturbations ($\sigma_8$) or the total matter density ($\Omega_{\rm m}$). Using current data and applying conservative assumptions about baryonic effects, we show that the observed velocity function of the Local Volume favours cosmologies in tension with the measurements from Planck but in agreement with the latest findings from weak lensing surveys. While the current systematics regarding the relation between observed and true rotation velocities are potentially important, upcoming data from HI surveys as well as new insights from hydrodynamical simulations will dramatically improve the situation in the near future.