Neutrino Mass Constraint from an Implicit Likelihood Analysis of BOSS Voids

Abstract

Cosmic voids identified in the spatial distribution of galaxies provide complementary information to two-point statistics. In particular, constraints on the neutrino mass sum, ∑ m _ν , promise to benefit from the inclusion of void statistics. We perform inference on the CMASS Northern Galactic Cap sample of the third-generation Sloan Digital Sky Survey/Baryon Oscillation Spectroscopic Survey (BOSS) with the aim of constraining ∑ m _ν . We utilize the void size function, the void–galaxy cross power spectrum, and the galaxy auto power spectrum. To extract constraints from these summary statistics we use a simulation-based approach, specifically implicit likelihood inference. We populate approximate gravity-only, particle-neutrino cosmological simulations with an expressive halo occupation distribution model. With a conservative scale cut of ${k}_{\max }=0.15\,h\,{\mathrm{Mpc}}^{-1}$ and a Planck-inspired Lambda cold dark matter prior, we find upper bounds on ∑ m _ν of 0.43 and 0.35 eV from the galaxy auto power spectrum and the full data vector, respectively (95% credible interval). Relaxing the scale cut to ${k}_{\max }=0.2\,h\,{\mathrm{Mpc}}^{-1}$ , we find 0.28 and 0.32 eV. Generally, void statistics appear to add modest but nonzero information beyond the auto power spectrum. We also substantiate the usual assumption that the void size function is Poisson distributed.

Keywords

• Redshift surveys
• Voids
• Cosmological neutrinos
• Neutrino masses
• N-body simulations
• Neural networks