Constraining M_ν 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, M_ν, a key parameter in particle physics beyond the Standard Model. However, degeneracies among cosmological parameters, especially between M_ν 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 M_ν 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 M_ν-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 {Ω_m, Ω_b, h, n_s, σ₈, M_ν}. For k_max=0.5 H/Mpc, the bispectrum provides Ω_m, Ω_b, h, n_s, and σ₈ constraints 1.9, 2.6, 3.1, 3.6, and 2.6 times tighter than the power spectrum. For M_ν, 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 M_ν 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 M_ν.