Halo abundance and clustering in cosmologies with massive and asymmetric neutrinos

Abstract

Neutrinos are the most abundant fermions in the Universe and influence the formation of large-scale structure through both their non-zero masses and a possible chemical potential which can be described by a single asymmetry parameter. While most previous studies have focused on the impact of the neutrino mass, the role of neutrino asymmetry remains comparatively unexplored. In this work, we investigate how massive neutrinos ($M_ν=0-0.24\,\mathrm{eV}$) with a non-zero asymmetry parameter ($η^{2}=0-0.8$) modify the halo mass function (HMF) and halo bias using cosmological N-body simulations with cosmological parameters consistently refitted to CMB observations. We find that at all redshifts, neutrino mass suppresses the abundance of massive halos, whereas neutrino asymmetry enhances the HMF over a broad mass range. At z=0, the abundance of the most massive halos is reduced by up to ~30% in the largest-mass case ($M_ν=0.24\,\mathrm{eV}$), while neutrino asymmetry ($η^{2}=0.8$) produces a maximum ~5% enhancement. These effects become increasingly pronounced at higher redshifts: by z=4 and z=9, the enhancement induced by neutrino asymmetry reaches ~25% and ~75%, respectively, while the corresponding suppression due to neutrino mass deepens to below ~40% and ~70% of the massless case. For halo bias, we find that halos with masses above $10^{13.4}\,\mathrm{M_\odot}$ exhibit an enhanced large-scale bias due to neutrino mass, reaching up to ~5% at z=0, while neutrino asymmetry reduces the bias by a few percent on linear scales. These trends strengthen with redshift, with the enhancement and suppression growing to ~15% and ~10% at z=2, respectively. Linear bias models provide an adequate, though not exact, description of halo bias in massive-neutrino cosmologies. Our results demonstrate that halo abundance and clustering offer sensitive probes of both neutrino mass and asymmetry.

Figures (7)

• Figure 1: Linear power spectrum (top panels) and mass variances (bottom panels) of CDM at $z=0$. Different colors and line styles correspond to different neutrino masses and asymmetry parameters, with the massless neutrino model adopted as the fiducial reference. Massive neutrinos suppress power spectra on small scales, while neutrino asymmetry parameter partially counteracts this suppression through the associated refitting of cosmological parameters required to maintain consistency with CMB observations.
• Figure 2: HMFs across redshifts $z=0-9$. The top panels compare HMFs measured from the simulations with predictions from the refitted MICE model, while the lower seven rows of panels show the corresponding fractional residuals. Symbols denote simulation measurements and curves represent the refitted model predictions, with consistent colors indicating the same cosmology. Redshift values are labeled next to the corresponding curves in the top panels. The refitted MICE model accurately reproduces the HMF over the whole mass and redshift ranges probed, with deviations well within statistical uncertainties.
• Figure 3: Impact of neutrinos on the HMF. Shown are the relative effects of neutrino mass and asymmetry on the HMF, as predicted by the refitted model (curves) and measured from simulations (symbols), normalized to the massless neutrino case. The curves and symbols with the same color correspond to the same cosmology. Panels from top to bottom correspond to increasing redshift. Increasing the neutrino mass systematically suppresses the abundance of massive halos at all redshifts. In contrast, variations in the neutrino asymmetry act in the opposite direction, enhancing the halo abundance over a broad mass range.
• Figure 4: Non-linear halo auto-power spectrum. The top panels show measurements from the $S_1$ simulation suite for halos with $M>10^{13.4}\,\mathrm{M_\odot}$ over redshifts $z=0-2$, with error bars indicating Poisson uncertainties and redshift labels placed next to each curve. The lower four rows of panels display the fractional differences relative to the massless neutrino case. Neutrino mass enhances the halo power spectrum amplitude, whereas a non-zero asymmetry parameter leads to a suppression, with model differences becoming increasingly pronounced toward higher redshift.
• Figure 5: Halo bias relative to the CDM density field. The top panels show the halo bias measured from the $S_1$ simulations for halos with $M>10^{13.4}\,\mathrm{M_\odot}$ over the redshift range $z=2$ to $z=0$, with the corresponding redshifts labeled in the upper left of each curve. The lower four rows of panels present fractional differences relative to the massless neutrino model. While the qualitative trends follow those seen in the halo power spectrum, the amplitudes differ, reflecting the combined influence of neutrinos on halo clustering and the underlying CDM density field.