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 BLᵐ(k₁, μ , t), 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 ~ 2~\ per\ cent for a total mass ∑ m_ν = 0.12\, eV. 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 B₀⁰ and B₂⁰ are found to be detectable with SNR 5 across a range of configurations, even after accounting for small-scale suppression. Higher order multipoles such as B₂¹ and B₂² are moderately sensitive, with SNR ($2-3$) in squeezed limits, while hexadecapole moments are more suppressed but still exhibit measurable signals at high k₁. Additionally, the SNR generally increases with wavenumber k₁, 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.