The imprints of massive neutrinos on the three-point correlation function of large-scale structures

¹ Dipartimento di Fisica e Astronomia “Augusto Righi”, Università di Bologna, Via Piero Gobetti 93/2, I-40129 Bologna, Italy
² INAF–Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Via Piero Gobetti 93/3, I-40129 Bologna, Italy
³ INAF-Osservatorio Astronomico di Brera, Via Brera 28, I-20122 Milano, Italy
⁴ INFN-Sezione di Genova, Via Dodecaneso 33, I-16146 Genova, Italy
⁵ Dipartimento di Fisica, Università di Genova, Via Dodecaneso 33, I-16146 Genova, Italy

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 22 December 2025
Accepted: 25 February 2026

Abstract

Aims. Free-streaming of cosmic neutrinos affects the distribution and growth of cosmic structures on small scales. This enables the sum of neutrino masses M_ν to be constrained from clustering studies. We investigate the possibility of disentangling massive neutrino cosmologies with the three-point correlation function (3PCF) for the first time.

Methods. We measured the isotropic connected 3PCF ζ and the reduced 3PCF Q of halo catalogs from the QUIJOTE suite of N-body simulations, considering M_ν = 0.0, 0.1, 0.2, and 0.4 eV in different redshift bins. We developed a framework to quantify the detectability of massive neutrinos for different triangle configurations and shapes, and applied it to a case compatible with a stage-IV spectroscopic survey. We also compared our results with the analysis of simulations without neutrinos, but with different σ₈ values, to test whether the 3PCF can break the well-known degeneracy between the two parameters.

Results. We found that as a result of free-streaming, the strongest signal is found for quasi-isosceles and squeezed triangles; this signal increases for decreasing redshifts. Among these configurations, elongated triangles, tracing the filamentary structure of the cosmic web, are the most affected by massive neutrinos, with a 3PCF signal increasing with M_ν. A complementary source of signal comes from right-angled triangles in Q. Importantly, we found that the signatures of a σ₈ variation appear to be significantly different on elongated triangles in ζ and right-angled triangles in Q, suggesting that the 3PCF can be used to effectively break the M_ν − σ₈ degeneracy. These results open the possibility to use the 3PCF as a powerful complementary tool for constraining neutrino masses in current and future spectroscopic surveys such as DESI, Euclid, 4MOST, and the Nancy Grace Roman Space Telescope.