Constraining effective neutrino species with bispectrum of large scale structures

TL;DR

This paper forecasts how galaxy bispectrum measurements can improve constraints on the effective number of neutrino species, $N_{eff}$, beyond current CMB limits, using Fisher analysis and BAO features.

Contribution

It demonstrates that bispectrum data from galaxy surveys can enhance $N_{eff}$ constraints, introducing a method to select informative triangle configurations to reduce computational costs.

Findings

Adding bispectrum data improves $N_{eff}$ constraints by 10-40% over Planck alone.

Combining bispectrum with power spectrum yields 5-30% further improvement.

Using BAO interference features allows efficient data analysis with minimal information loss.

Abstract

Relativistic and free-streaming particles like neutrinos leave imprints in large scale structures (LSS), providing probes of the effective number of neutrino species $N_{\rm eff}$. In this paper, we use the Fisher formalism to forecast $N_{\rm eff}$ constraints from the bispectrum (B) of LSS for current and future galaxy redshift surveys, specifically using information from the baryon acoustic oscillations (BAOs). Modeling the galaxy bispectrum at the tree-level, we find that adding the bispectrum constraints to current CMB constraints from Planck can improve upon the Planck-only constraints on $N_{\rm eff}$ by about 10\% -- 40\% depending on the survey. Compared to the Planck + power spectrum (P) constraints previously explored in the literature, using Planck+P+B provides a further improvement of about 5\% -- 30\%. Besides using BAO wiggles alone, we also explore using the total information which includes both the wiggles and the broadband information (which is subject to systematics challenges), generally yielding better results. Finally, we exploit the interference feature of the BAOs in the bispectrum to select a subset of triangles with the most information on $N_{\rm eff}$. This allows for the reduction of computational cost while keeping most of the information, as well as for circumventing some of the shortcomings of applying directly to the bispectrum the current wiggle extraction algorithm valid for the power spectrum. In sum, our study validates that the current Planck constraint on $N_{\rm eff}$ can be significantly improved with the aid of galaxy surveys before the next-generation CMB experiments like CMB-Stage 4.