Constraining $M_\nu$ with the Bispectrum 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, $M_\nu$, a key parameter in particle physics beyond the Standard Model. However, degeneracies among cosmological parameters, especially between $M_\nu$ and $\sigma_8$, limit the constraining power of standard two-point clustering statistics. In this work, we investigate whether we can break these degeneracies and constrain $\smnu$ 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 $M_\nu$--$\sigma_8$ 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 $\{\Omega_m$, $\Omega_b$, $h$, $n_s$, $\sigma_8$, $M_\nu\}$. For $k_{\rm max}{=}0.5~h/{\rm Mpc}$, the bispectrum provides $\Omega_m$, $\Omega_b$, $h$, $n_s$, and $\sigma_8$ constraints 1.9, 2.6, 3.1, 3.6, and 2.6 times tighter than the power spectrum. For $M_\nu$, the bispectrum improves the 1$\sigma$ constraint from 0.2968 to 0.0572 eV --- over 5 times tighter than the power spectrum. Even with priors from {\em Planck}, the bispectrum improves $M_\nu$ 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 $(1~h^{-1}{\rm Gpc})^3$ 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 $M_\nu$.