The Neutrino Puzzle: Anomalies, Interactions, and Cosmological Tensions

TL;DR

This work investigates whether self-interactions among massive neutrinos can delay their early-Universe free-streaming and alleviate tensions between CMB inferences and late-time measurements of the Hubble constant $H_0$ and matter fluctuations $\sigma_8$. Using a simplified massive-neutrino interaction model with a four-fermion coupling $G_{\rm eff}$, the authors solve modified Boltzmann equations and fit to Planck, BAO, and local $H_0$ data with $N_{\rm eff}$ and $\sum m_\nu$ as free parameters. They identify two modes—strongly and moderately interacting neutrinos—characterized by distinct $N_{\rm eff}$, $\sum m_\nu$, and $G_{\rm eff}$, achieving $H_0\approx 72.3$ km s$^{-1}$ Mpc$^{-1}$ and $\sigma_8\approx 0.786$ in the SI$\nu$ case, albeit with nuanced Bayesian evidence. The results illustrate that radically different cosmological scenarios can provide excellent data fits and motivate further exploration of neutrino microphysics, polarization data impacts, and more flexible helium and nuisance-parameter treatments to robustly test these ideas.

Abstract

New physics in the neutrino sector might be necessary to address anomalies between different neutrino oscillation experiments. Intriguingly, it also offers a possible solution to the discrepant cosmological measurements of $H_0$ and $σ_8$. We show here that delaying the onset of neutrino free-streaming until close to the epoch of matter-radiation equality can naturally accommodate a larger value for the Hubble constant $H_0=72.3 \pm 1.4$ km/s/Mpc and a lower value of the matter fluctuations $σ_8=0.786\pm 0.020$, while not degrading the fit to the cosmic microwave background (CMB) damping tail. We achieve this by introducing neutrino self-interactions in the presence of a non-vanishing sum of neutrino masses. This strongly interacting neutrino cosmology prefers $N_{\rm eff} = 4.02 \pm 0.29$, which has interesting implications for particle model-building and neutrino oscillation anomalies. We show that the absence of the neutrino free-streaming phase shift on the CMB can be compensated by shifting the value of other cosmological parameters, hence providing an important caveat to the detections made in the literature. Due to their impact on the evolution of the gravitational potential at early times, self-interacting neutrinos and their subsequent decoupling leave a rich structure on the matter power spectrum. In particular, we point out the existence of a novel localized feature appearing on scales entering the horizon at the onset of neutrino free-streaming. While the interacting neutrino cosmology provides a better global fit to current cosmological data, we find that traditional Bayesian analyses penalize the model as compared to the standard cosmological. Our analysis shows that it is possible to find radically different cosmological models that nonetheless provide excellent fits to the data, hence providing an impetus to thoroughly explore alternate cosmological scenarios.

Figures (12)

• Figure 1: Effects of $\sum m_\nu$, $G_\mathrm{eff}$, and $N_{\rm eff}$ on the phase and amplitude of the TT and EE power spectra. Colors denote different values of $G_\mathrm{eff}$. Solid spectra correspond to $\sum m_\nu=0.06\,\mathrm{eV}$ and dashed spectra correspond to $\sum m_\nu=0.23\,\mathrm{eV}$. Measurements from the Planck 2015 data release are included planckCMB.
• Figure 2: The evolution of the $\psi$ gravitational potential (left) and of the gauge invariant dark matter density contrast $d_{\rm c}$ (right) for different $k$-modes as a function of redshift. Solid lines correspond to the interacting neutrino case with $G_{\rm eff} = 10^{-2}$ MeV$^{-2}$, $N_{\rm eff}= 3.046$, and $\sum m_\nu=0.06$ eV, whereas dashed lines correspond to the $\Lambda\mathrm{CDM}$ case. On the left, we plot $-3\psi/(2\zeta)$, where $\zeta$ is the gauge-invariant curvature perturbation. The lower left panel shows the normalized difference between the interacting neutrino and $\Lambda$CDM $\psi$ potential, while the lower right panel shows the ratio of the dark matter fluctuations in the two models. The onset of neutrino free-streaming for the interacting neutrino model shown here occurs at $z_{\rm dec,\nu}\simeq 10^4$. Dark matter fluctuations entering the horizon while neutrinos are still tightly coupled decay and appear damped at present relative to $\Lambda \mathrm{CDM}$, while those entering the horizon during neutrino decoupling receive a net boost that persists until the present epoch.
• Figure 3: Effects of $G_\mathrm{eff}$, $\sum m_\nu$, and $N_{\rm eff}$ on the matter power spectrum. Colors denote different values of $G_\mathrm{eff}$. Solid spectra correspond to $\sum m_\nu=0.06\,\mathrm{eV}$ and dashed spectra correspond to $\sum m_\nu=0.23\,\mathrm{eV}$. Dotted lines in the bottom panel have $N_{\rm eff}=4.046$. Note the localized increase in amplitude at the scales entering the horizon at the onset of neutrino free-streaming.
• Figure 4: 2D posteriors for $S_8$ and $H_0$ illustrating how neutrino self-interactions can remedy cosmological tensions. We compare the Planck $\mathrm{TT+lens+BAO}$$\Lambda \mathrm{CDM}$ posterior to the $\mathrm{SI}\nu$ and $\mathrm{MI}\nu$ posteriors for $\mathrm{TT+lens+BAO}$. We overlay $2\sigma$ bands for the measurements $S_8 = 0.427 \pm 0.016$Hikage:2018qbn and $H_0 = 73 \pm 1.75$ km/s/Mpc HST.
• Figure 5: 1D posteriors for the TT+lens+BAO+$H_0$ data combination after separating the $\mathrm{SI}\nu$ and $\mathrm{MI}\nu$ modes and plotting them independently. For this reason, the peak locations and posterior shapes are of physical interest rather than the relative heights of the peaks.