Redshift-space galaxy bispectrum in presence of massive neutrinos: a multipole expansion approach for Euclid

Massive neutrinos imprint distinctive signatures on the evolution of cosmic structures, notably suppressing small-scale clustering. We investigate the impact of massive neutrinos on the galaxy bispectrum in redshift space, adopting a spherical harmonic multipole decomposition, that captures the full angular dependence. We develop an analytical and numerical framework incorporating neutrino-corrected perturbation theory kernels and redshift-space distortions. Our results demonstrate that the linear triangle configurations are particularly sensitive to massive neutrinos, with deviations reaching up to for a total mass. To assess detection prospects in galaxy surveys like Euclid, we compute the signal-to-noise ratio (SNR) for individual multipoles, including the effects of Finger-of-God damping and shot noise. The neutrino-induced signatures in and are found to be detectable with SNR across a range of configurations, even after accounting for small-scale suppression. Higher order multipoles such as and are moderately sensitive, with SNR () in squeezed limits, while hexadecapole moments are more suppressed but still exhibit measurable signals at high. Additionally, the SNR generally increases with wavenumber, particularly for squeezed and stretched triangles, suggesting that access to smaller scales significantly enhances detection prospects. Our study highlights the potential of the redshift-space bispectrum multipoles as sensitive probes of massive neutrinos, complementing traditional power spectrum analyses, and underscores the importance of angular information and higher order statistics for galaxy surveys.