7.3. Constraints on the νCDM Cosmology

Albeit their small size and mass, the left-handed neutrinos influence the formation of large-scale structure by hindering the formation of small-scale haloes and leaving their imprints on the gravitational collapse process. The relative number of low-mass haloes in cluster abundance measurements can shed light on the summed masses of three left-handed neutrino species. With the discovery of neutrino oscillations between different flavors, electron, muon, and tau neutrinos, it has become clear that neutrino eigenstates must have non-zero mass (Fukuda et al. 1998; Ahmad et al. 2002). The theoretical predictions indicate a hierarchical relation between the mass eigenstates of the three species of neutrinos; however, their ordering in mass remains elusive. Based on the normal neutrino mass hierarchy model, the third neutrino mass eigenstate, associated with the tau neutrino, is the heaviest among the three. This is followed by the eigenstate of the muon neutrino, which has an intermediate-mass, and that of the electron neutrino, i.e., mτ >mµ >me. The ordering is swapped in the inverted mass hierarchy model such that mτ < mµ<me. Recent constraints of their summed mass show that the lower limit provided by the oscillation experiments depends on the assumed underlying hierarchy model (Qian &Vogel 2015; Esteban et al. 2020), with a lower limit of mν >0.059eV for normal mass hierarchy and mν>0.101eV for the inverted hierarchy models (Tanabashi et al. 2018; Athar et al. 2022). Constraining the summed mass to <0.1eV implies that the inverted model is excluded. The ground-based experiments through beta decay of tritium imply the sum to be mν <1.1eV at 90% confidence level, a narrow range for the allowed summed mass (Aker et al. 2019). The space-based Planck CMB measurements provide a similar upper limit of mν<0.26 eV at 95% confidence level (Planck Collaboration et al. 2020a). As we probe the largest collapsed objects in the Universe, galaxy clusters, the cluster number counts can be used to constrain the summed masses of the neutrinos. To do so, we allow the sum of neutrino masses to be free in the cosmology pipeline, with a uniform prior of U(0eV,1eV). We stress that our lower limit is set to 0eV instead of a value of 0.059eV (Tanabashi et al. 2018) adopted by the PlanckCMB 2020 analysis. As the lower limit on the neutrino mass depends on the assumptions of the neutrino mass model, we do not make any prior assumptions about its value and adopt uniform priors on its value to avoid this parameter from affecting our posterior distributions. The cosmological constraints with free neutrino mass components are;

Ωm=0.29+0.01 −0.02

σ8=0.87±0.02

S8=0.86±0.01

mν<0.22eV (95% CL) (36)

These results are visualized in Fig.11. The upper limit to the sum of neutrino masses is mν <0.22eV. Our results represent the tightest limits on the sum of neutrino masses from cluster abundance experiments; for instance, the SPT-SZ sample results in an upper limit of <0.74eV(95% confidence interval) (Bocquet et al. 2019). The eROSITA upper limits on the neutrino masses are competitive and informative at a similar precision with thePlanckCMB2020 measurements, mν < 0.26eV (95%CL) (Planck Collaboration et al. 2020a). We verify that the values of the Ωm and σ8 remain statistically consistent when mν is allowed to be non-zero, see Fig.B.4. We find that eRASS1 and PlanckCMBνCDM parameters are consistent at the 2.0σ level.

Given the excellent agreement with PlanckCMB measurements, the resulting cosmological parameters of two probes can be combined in a statistically meaningful way, enabling a much tighter measurement of the impact of massive neutrinos on both the formation and evolution of the large-scale structure and on the primordial density field. As performed in the ΛCDM analysis, we combine our results with the PlanckCMB constraints to break the degeneracy between Ωm and σ8. We obtain;

Ωm=0.32±0.01

σ8=0.83±0.01

S8=0.85±0.01

mν<0.11eV (95% CL) (37)

Simultaneously fitting our measurements with Planck CMB 2020 likelihood chains yield an upper limit of mν < 0.11eV, consistent with the results in the literature results with marginally consistent with the inverted mass hierarchy model, which requires mν > 0.101eV.

As a final step, we combine eRASS1 cluster abundance measurements through importance sampling with PlanckCMB and with the lower limits from ground-based oscillation experiments (Tanabashi et al. 2018).

In the case of a normal mass hierarchy scenario, the summed masses of mν=0.08 +0.03 −0.02eV, while assuming the inverted mass hierarchy model, we obtain summed masses of mν =0.12 +0.03 −0.01eV.It is interesting to point out, from Fig.C.1, that the constraints on the mass of the lightest neutrino eigenstates are similar: for both mass hierarchy we obtain

m(light) = 0.01 +0.020 −0.005 eV (68% confidence intervals) or with an upper limit of 0.04 eV.

## Wednesday, February 14, 2024

### New Cosmology Bounds On Neutrino Mass

In V. Ghirardini, et al., "The SRG/eROSITA All-Sky Survey: Cosmology Constraints from Cluster Abundances in the Western Galactic Hemisphere" arxiv.org/abs/2402.08458 (Feb. 13, 2023), a major new dataset constrains the possible range of the sum of the three neutrino masses.

The best fit value of the lightest neutrino mass eigenstate (considering both cosmology and oscillation data) is 1 meV, with a range of 0-5 meV at the 95% confidence level.

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