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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 $γ$. We arrive at the following marginalized constraints: $σ_8 = 0.65^{+0.23}_{-0.37}$ and $γ= 1.38^{+1.7}_{-0.65}$. Assuming instead GR as the correct gravitation theory (and thus $γ\equiv 0.55$), the constraints in $σ_8$ tighten further: $σ_8 = 0.40^{+0.21}_{-0.23}$. We show that these constraints complement well the ones obtained from other datasets and that they could improve substantially with more SNe.