Constraining M-nu with the bispectrum. Part I. Breaking parameter degeneracies

Massive neutrinos suppress the growth of structure below their free-streaming scale and leave an imprint on large-scale structure. Measuring this imprint allows us to constrain the sum of neutrino masses, Mν, a key parameter in particle physics beyond the Standard Model. However, degeneracies among cosmological parameters, especially between Mν and σ8, limit the constraining power of standard two-point clustering statistics. In this work, we investigate whether we can break these degeneracies and constrain Mν with the next higher-order correlation function-the bispectrum. We first examine the redshift-space halo bispectrum of 800 N-body simulations from the HADES suite and demonstrate that the bispectrum helps break the Mν-σ8 degeneracy. Then using 22,000 N-body simulations of the Quijote suite, we quantify for the first time the full information content of the redshift-space halo bispectrum down to nonlinear scales using a Fisher matrix forecast of {Ωm, Ωb, h, ns, σ8, Mν}. For kmax=0.5 H/Mpc, the bispectrum provides Ωm, Ωb, h, ns, and σ8 constraints 1.9, 2.6, 3.1, 3.6, and 2.6 times tighter than the power spectrum. For Mν, the bispectrum improves the 1σ constraint from 0.2968 to 0.0572 eV-over 5 times tighter than the power spectrum. Even with priors from Planck, the bispectrum improves Mν constraints by a factor of 1.8. Although we reserve marginalizing over a more complete set of bias parameters to the next paper of the series, these constraints are derived for a (1 h-1Gpc)3 box, a substantially smaller volume than upcoming surveys. Thus, our results demonstrate that the bispectrum offers significant improvements over the power spectrum, especially for constraining Mν