Turning noise into signal: learning from the scatter in the Hubble diagram

Abstract

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: ${\sigma }_8=0.65_{-0.37}^{+0.23}$ and $\gamma =1.38_{-0.65}^{+1.7}$. Assuming instead GR as the correct gravitation theory (and thus $\gamma \equiv 0.55$), the constraints in ${\sigma }_8$ tighten further: ${\sigma }_8=0.40_{-0.23}^{+0.21}$. We show that these constraints complement well the ones obtained from other datasets and that they could improve substantially with more SNe.

v2: Real data results corrected; forecast for future data added; discussion extended. v3: Improved discussion; matches published version. 8 figs 15 pages

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• Machine learning phases and criticalities without using real data for training
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• Joint Curvature and Growth Rate measurements with Supernova Peculiar Velocities and the CMB
• First constraints on the intrinsic CMB dipole and our velocity with Doppler and aberration