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 $M < 10^9
M_{\odot}$.
