Turning noise into signal: learning from the scatter in the Hubble
  diagram
  The supernova (SN) Hubble diagram residual contains valuable information on
both the present matter power spectrum and its growth history. In this paper we
show that this information can be retrieved with precision by combining both
peculiar velocity and weak-lensing analysis on the data. To wit, peculiar
velocity induces correlations on the nearby SN while lensing induces a
non-Gaussian dispersion in faraway objects. We show that both effects have
almost orthogonal degeneracies and discuss how they can be extracted
simultaneously from the data. We analyze the JLA supernova catalog in a
14-dimensional parameter space, assuming a flexible growth-rate index $\gamma$.
We arrive at the following marginalized constraints: $\sigma_8 =
0.65^{+0.23}_{-0.37}$ and $\gamma = 1.38^{+1.7}_{-0.65}$. Assuming instead GR
as the correct gravitation theory (and thus $\gamma \equiv 0.55$), the
constraints in $\sigma_8$ tighten further: $\sigma_8 = 0.40^{+0.21}_{-0.23}$.
We show that these constraints complement well the ones obtained from other
datasets and that they could improve substantially with more SNe.
