Constraining <i>M</i><sub>ν</sub> with the bispectrum. Part I. Breaking parameter degeneracies
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
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 $M_\nu$.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it