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 on I find that information rises again in the highly non-linear regime. I find that the cosmological information in this small scale miracle can indeed be disentangled from astrophysical information and yield large improvements. Pushing SKA2 analysis from kmax=1 Mpc$^{-1}$ to kmax=10 Mpc$^{-1}$ can improve the error bar on $sigma_8$ by a factor 9 and the error bar on the Dark Energy equation of state $w_0$ by a factor 5. Finally I show that high order statistics beyond the power spectrum should yield further significant improvements in this regime, with the improvements increasing when pushing kmax. Data and notebooks reproducing all plots and results will be made available at url{https://github.com/fabienlacasa/SmallScaleMiracle}