Implications for the missing low-mass galaxies (satellites) problem from cosmic shear

The number of observed dwarf galaxies, with dark matter mass $\lesssim 10^{11}$ M$_{\odot}$ in the Milky Way or the Andromeda galaxy does not agree with predictions from the successful $\Lambda$CDM paradigm. To alleviate this problem a suppression of dark matter clustering power on very small scales has been conjectured. However, the abundance of dark matter halos outside our immediate neighbourhood (the Local Group) seem to agree with the $\Lambda$CDM--expected abundance. Here we connect these problems to observations of weak lensing cosmic shear, pointing out that cosmic shear can make significant statements about the missing satellites problem in a statistical way. As an example and pedagogical application we use recent constraints on small-scales power suppression from measurements of the CFHTLenS data. We find that, on average, in a region of $\sim$Gpc$^3$ there is no significant small-scale power suppression. This implies that suppression of small-scale power is not a viable solution to the `missing satellites problem' or, alternatively, that on average in this volume there is no `missing satellites problem' for dark matter masses $\gtrsim 5 \times 10^9$ M$_{\odot}$. Further analysis of current and future weak lensing surveys will probe much smaller scales, $k > 10h$ Mpc$^{-1}$ corresponding roughly to masses $M < 10^9 M_{\odot}$.