In the Standard Model, neutrinos are massless. However, oscillation experiments demonstrate that they do have a small mass. Currently, only the differences of the masses squared are known, along with an upper bound on their sum. Upcoming surveys of the Universe’s Large-Scale Structure offer a promising avenue to probe neutrino mass by revealing how neutrinos influence galaxy clustering. Massive neutrinos affect mode coupling within the framework of Perturbation Theory (PT) for structure formation, leaving detectable signatures in the PT kernels. In this work, we present for the first time the explicit modifications to the kernels caused by massive neutrinos and investigate the extent of these changes in the redshift-space galaxy bispectrum. To this end, we generate synthetic data using a theoretical covariance matrix and employ Markov-chain Monte Carlo to assess the impact of these new signature terms. This approach, in contrast to Fisher forecasting, allows us to see if the new terms induce shifts in the recovered central values of parameters. The synthetic data are produced to mirror two different galaxy samples. The first corresponds to the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey Data Release 12 CMASS Luminous Red Galaxy (LRG) sample, characterized by an effective volume of $V_{\mathrm{eff}}=3[\mathrm{Gpc}/h{]}^3$ and a number density of $\overline{n}=3\times {10}^{-4}h/\mathrm{Mpc}$. The second corresponds to the Dark Energy Spectroscopic Instrument (DESI) Year 5 LRG sample with $V_{\mathrm{eff}}=25[\mathrm{Gpc}/h{]}^3$. Our findings indicate that neglecting neutrino mass effects in the kernels can result in a central value shift equivalent to approximately $1\sigma$ in the galaxy biases estimated from the DESI Y5-like sample and no observable shift of the cosmological parameters.

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• Cosmological parameters
• Cosmology
• Large scale structure of the Universe