Extra Radiation Cosmologies: Implications of the Hubble Tension for eV-scale Neutrinos

TL;DR

This paper investigates sterile neutrino cosmologies in the context of the Hubble tension by combining DESI DR2 BAO with CMB, lensing, and supernova data. It shows that BAO observables are comparatively insensitive to simultaneous variations in $N_{\rm eff}$ and $\Sigma m_\nu$, enabling a joint analysis that yields $N_{\rm eff}\approx3.4$–$3.5$ and tight bounds on sterile masses when the data include SH0ES $H_0$. A representative 0.1 eV sterile neutrino yields $N_{\rm eff}=3.50$ with an upper limit $m_s<0.170$ eV (95% CL), relaxing the standard $\Sigma m_\nu$ constraint by about a factor of 4.3 and favoring light, partially thermalized sterile states at $\gtrsim3\sigma$ with SH0ES data, while fully eV-scale masses remain disfavored. The work highlights prior-volume effects in Bayesian mapping of $m_s$, underscores a tension with short-baseline oscillation hints, and points to future DESI and CMB-S4 data as crucial for resolving the sterile neutrino contribution to the cosmic energy budget and the $H_0$ tension.

Abstract

We present a new analysis on sterile neutrino cosmologies using the Dark Energy Spectroscopic Instrument (DESI) second data release (DR2) baryon acoustic oscillation (BAO) measurements in combination with cosmic microwave background (CMB), CMB lensing, and supernova data. We show that BAO observables are intrinsically less sensitive to the combined effects of relativistic energy density, $N_{\rm eff}$, and the sum of neutrino masses, $Σm_ν$, which are both augmented in sterile neutrino cosmologies. With SH0ES local expansion rate, $H_0$, data, we find $N_{\rm eff} = 3.43 \pm 0.13$, reducing the Hubble tension to $2.4σ$. For a 0.1 eV sterile neutrino, we find $N_{\rm eff}=3.50$ as the best fit. For this representative $N_{\rm eff}$, we find an upper limit of $m_s < 0.17$ eV (95% CL), greater than a factor of four weaker than standard constraints on $Σm_ν$. When SH0ES is included, light sterile neutrinos with masses $m_s\simeq0.1$-$0.2$ eV are favored at $\gtrsim 3σ$, whereas eV-scale sterile masses remain strongly excluded by the data in the cosmologies we study. Our findings confirm our previous results that partially thermalized sub-eV sterile neutrinos are preferred by the SH0ES $H_0$ data. The preferred $m_s$ mass scale overlaps with, but is not identical to, that favored in neutrino oscillation solutions to short-baseline anomalies.

Figures (5)

• Figure 1: Left panel: contours of the clustering amplitude $\sigma_8$ as a function of the total neutrino mass $\Sigma m_\nu$ and the effective number of relativistic species $N_{\mathrm{eff}}$, computed while keeping the remaining $\Lambda$CDM parameters fixed at their standard values. Lowering $\Sigma m_\nu$ and $N_{\mathrm{eff}}$ increases $\sigma_8$, while raising them decreases it. Right panel: contours of the BAO distance ratio $D_\mathrm{M}/r_\mathrm{d}$ at $z=0.51$ for different $\Sigma m_\nu$ and $N_{\mathrm{eff}}$ values when the total matter density is fixed. An increase in neutrino mass is compensated by a reduction in the cold dark matter fraction. These contours reveal the anticorrelated response of $\Sigma m_\nu$ and $N_{\mathrm{eff}}$ through their opposite effects on the $D_\mathrm{M}/r_\mathrm{d}$ BAO observable. Together, these panels highlight the complementary ways in which neutrino properties imprint on growth and geometry.
• Figure 2: Top Panels:$D_\mathrm{M}/r_\mathrm{d}$ shown along the horizontal axis and $D_\mathrm{H}/r_\mathrm{d}$ along the vertical axis, calculated from the parameters of the MCMC chains from the Planck 2018 CMB likelihoods alone, for two distinct models with free neutrino mass and $N_\mathrm{eff}$, separately. The left panel corresponds to a redshift of 0.51 and the right panel to a redshift of 2.33. The colors indicate the values of $N_\mathrm{eff}$ and $\Sigma m_\nu$ specified in the color bar. A positive vertical offset has been applied to the $\Sigma m_\nu$ chains in both panels to ensure clarity of the figure ($z=0.51$ vertical offset of $+1$ ; $z=2.33$ vertical offset of $+0.2$). The purple contours denote the $1\sigma$ and $2\sigma$ DESI DR2 BAO measurements of $D_\mathrm{M}/r_\mathrm{d}$ and $D_\mathrm{H}/r_\mathrm{d}$. Bottom Panels: To show their dependence on the neutrino parameters independent of $r_\mathrm{d}$, $D_\mathrm{M}$ is shown along the horizontal axis and $D_\mathrm{H}$ is along the vertical axis for models with free neutrino mass and $N_\mathrm{eff}$, including only the Planck 2018 CMB likelihoods. A positive vertical offset of +100 Mpc has been applied to the $\Sigma m_\nu$ chain points at $z=0.51$ to ensure clarity of the figure.
• Figure 3: Variation of the transverse distance $D_\mathrm{M}$ (solid lines) and the radial distance $D_\mathrm{H}$ (dashed lines) is shown at two redshifts: $z=0.51$ (blue) and $z=2.33$ (red). These are plotted as the Hubble constant $H_0$ along the lower horizontal axis and the matter density $\Omega_m$ are varied along their linear degeneracy from the Planck 2018 CMB likelihoods, as described in the text. The left panel shows models where $\Sigma m_\nu$ increases in correlation with $\Omega_m$ (to the left) and the right panel shows models where $N_\mathrm{eff}$ increases in anticorrelation to $\Omega_m$, to the right.
• Figure 4: We show the profile likelihood for the physical sterile neutrino mass $m_s$, with the effective number of neutrino species fixed to $N_{\rm eff} = 3.50$. The red points show the computed $\Delta \chi^2$ values at discrete mass points used in the fit, while the blue curve represents a parabolic interpolation through these points. Shaded bands indicate the 68% (black) and 95% (purple) confidence intervals, respectively.
• Figure 5: Two-dimensional posterior distributions are shown for the physical sterile neutrino mass, $m_{\rm s}$ and the effective number of neutrino species, $N_{\rm eff}$, under three different prior choices using MCMC Bayesian methods and our baseline datasets. The black contours correspond to a prior set as $1/\sqrt{m_s}$, the light purple contours to a prior as $1/m_s$, and the pale green contours, which give the most relaxed bounds, correspond to a prior of $1/m_s^2$. This figure illustrates the impact of prior volume effects in Bayesian analyses of this cosmological model.