Bias due to neutrinos must not uncorrect'd go

TL;DR

Massive neutrinos induce a scale-dependent galaxy bias when biasing is defined with respect to the total matter field, potentially biasing neutrino mass inferences from galaxy clustering. The authors advocate defining the bias with respect to the CDM+baryons field and provide a practical, RSD- and non-linear-aware prescription for the correction, implemented at the Boltzmann-solver level. Using MCMC forecasts with Planck-like and Euclid-like data, they show that neglecting the correction biases the inferred sum of neutrino masses $M_ν$ and propagates to correlated parameters such as $Ω_{cdm} h^2$ and $n_s$, while the corrected analysis recovers the fiducial value. They release a clear methodological framework and will provide publicly available tools in the CLASS code to enable robust corrections for future galaxy clustering analyses.

Abstract

In cosmologies with massive neutrinos, the galaxy bias defined with respect to the total matter field (cold dark matter, baryons, and non-relativistic neutrinos) depends on the sum of the neutrino masses $M_ν$, and becomes scale-dependent even on large scales. This effect has been usually neglected given the sensitivity of current surveys, but becomes a severe systematic for future surveys aiming to provide the first detection of non-zero $M_ν$. The effect can be corrected for by defining the bias with respect to the density field of cold dark matter and baryons instead of the total matter field. In this work, we provide a simple prescription for correctly mitigating the neutrino-induced scale-dependent bias effect in a practical way. We clarify a number of subtleties regarding how to properly implement this correction in the presence of redshift-space distortions and non-linear evolution of perturbations. We perform a MCMC analysis on simulated galaxy clustering data that match the expected sensitivity of the \textit{Euclid} survey. We find that the neutrino-induced scale-dependent bias can lead to important shifts in both the inferred mean value of $M_ν$, as well as its uncertainty. We show how these shifts propagate to other cosmological parameters correlated with $M_ν$, such as the cold dark matter physical density $Ω_{cdm} h^2$ and the scalar spectral index $n_s$. In conclusion, we find that correctly accounting for the neutrino-induced scale-dependent bias will be of crucial importance for future galaxy clustering analyses. We encourage the cosmology community to correctly account for this effect using the simple prescription we present in our work. The tools necessary to easily correct for the neutrino-induced scale-dependent bias will be made publicly available in an upcoming release of the Boltzmann solver \texttt{CLASS}.

Figures (2)

• Figure 1: One-dimensional marginalized posterior probabilities, normalized to their maximum values, of the sum of the active neutrino masses $M_{\nu}$ (in eV) for the two cases considered in this analysis: the correct case (blue solid), where the neutrino-induced scale-dependent bias (NISDB) correction is properly applied, and the wrong case (red dashed), where the NISDB correction is not applied. The dot-dashed vertical line at $M_{\nu}=0.06\,{\rm eV}$ shows the input fiducial value of $M_{\nu}$ used in our analysis. It is clearly visible that the input fiducial value is perfectly recovered for the blue curve (correct case). When the correction is not applied, we fail in recovering the input fiducial value, as shown by the red curve.
• Figure 2: Triangular plot showing joint and one-dimensional marginalized posterior distributions for the parameters which are most correlated with the sum of the three active neutrino masses $M_{\nu}$ (in eV). These parameters are the dark matter physical density $\omega_{cdm} \equiv \Omega_{cdm} h^2$ and the scalar spectral index $n_s$. The panels along the diagonal show the one-dimensional probability distributions of the individual parameters. The remaining blocks show the 2D joint distributions. The distributions are shown for two cases: the case where the neutrino-induced scale-dependent bias (NISDB) correction is properly applied (blue, 1D posteriors are given by solid curves), and the case where the NISDB correction is not applied (red, 1D posteriors are given by dashed curves). The one-dimensional distributions along the diagonal represent normalized probability distributions and are hence in arbitrary units.