Cosmology in the non-linear regime : the small scale miracle
  Interest rises to exploit the full shape information of the galaxy power
spectrum, as well as pushing analyses to smaller non-linear scales. Here I use
the halo model to quantify the information content in the tomographic angular
power spectrum of galaxies, for future high resolution surveys : Euclid and
SKA2. I study how this information varies as a function of the scale cut
applied, either with angular cut $\ell_{max}$ or physical cut kmax. For this, I
use analytical covariances with the most complete census of non-Gaussian terms,
which proves critical. I find that the Fisher information on most cosmological
and astrophysical parameters follows a striking behaviour. Beyond the
perturbative regime we first get decreasing returns : the information keeps
rising but the slope slows down until reaching a saturation. The location of
this plateau is a bit beyond the reach of current modeling methods : k $\sim$ 2
Mpc$^{-1}$ and slightly depends on the parameter and redshift bin considered. I
explain the origin of this plateau, which is due to non-linear effects both on
the power spectrum, and more importantly on non-Gaussian covariance terms.
Then, pushing further we see the information rising again in the highly
non-linear regime, with a steep slope. This is the small scale miracle, for
which I give interpretation and discuss the properties. Hints are shown that
this information should be disentanglable from the astrophysical content, and
could improve Dark Energy constraints. Finally, more hints are shown that high
order statistics may yield significant improvements over the power spectrum in
this regime, with the improvements increasing with kmax. Data and notebooks
reproducing all plots and results will be made available at
\url{https://github.com/fabienlacasa/SmallScaleMiracle}
