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.
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