A tale of two modes: Neutrino free-streaming in the early universe

TL;DR

The study tests whether cosmological neutrinos free-stream as in standard $\Lambda$CDM or exhibit self-interactions via a four-fermion coupling $G_{ m eff}$ that delays decoupling. It develops a Fermi-like interaction framework, modifies the neutrino Boltzmann hierarchy, and analyzes Planck 2015 TT/Pol, BAO, and $H_0$ data with nested sampling to map a bimodal posterior in $\log_{10}(G_{ m eff} {\rm MeV}^2)$. Two modes emerge: a dominant $\Lambda$CDM-compatible one with $\log_{10}(G_{ m eff} {\rm MeV}^2) < -3.60$ and an interacting mode around $\log_{10}(G_{ m eff} {\rm MeV}^2) \approx -1.72$, the latter peaking at $z_{\nu,\rm dec} \sim 8300$ and offering a partial alleviation of the $H_0$ tension. Bayesian evidence favors the standard mode, though the interacting mode gains relative weight when polarization and local $H_0$ are included, and Stage-IV CMB forecasts promise substantially tighter constraints on $G_{ m eff}$. The results imply neutrinos must free-stream long before matter–radiation equality, with future data needed to completely exclude or confirm late-time neutrino interactions.

Abstract

We present updated constraints on the free-streaming nature of cosmological neutrinos from cosmic microwave background (CMB) power spectra, baryonic acoustic oscillation data, and local measurements of the Hubble constant. Specifically, we consider a Fermi-like four-fermion interaction between massless neutrinos, characterized by an effective coupling constant $ G_{\rm eff}$, and resulting in a neutrino opacity $\dotτ_ν\propto G_{\rm eff}^2 T_ν^5$. Using a conservative prior on the parameter $\log_{10}\left(G_{\rm eff} {\rm MeV}^2\right)$, we find a bimodal posterior distribution. The first of these modes is consistent with the standard $Λ$CDM cosmology and corresponds to neutrinos decoupling at redshift $z_{ν,{\rm dec}} > 1.3\times10^5$. The other mode of the posterior, dubbed the "interacting neutrino mode", corresponds to neutrino decoupling occurring within a narrow redshift window centered around $z_{ν,{\rm dec}}\sim8300$. This mode is characterized by a high value of the effective neutrino coupling constant, together with a lower value of the scalar spectral index and amplitude of fluctuations, and a higher value of the Hubble parameter. Using both a maximum likelihood analysis and the ratio of the two mode's Bayesian evidence, we find the interacting neutrino mode to be statistically disfavored compared to the standard $Λ$CDM cosmology. Interestingly, the addition of CMB polarization and direct Hubble constant measurements significantly raises the statistical significance of this secondary mode, indicating that new physics in the neutrino sector could help explain the difference between local measurements of $H_0$, and those inferred from CMB data. A robust consequence of our results is that neutrinos must be free streaming long before the epoch of matter-radiation equality.

Figures (9)

• Figure 1: Posterior probability distribution of the parameter $\log_{10}\left( G_{\rm eff} {\rm MeV}^2\right)$, marginalized over all other cosmological parameters, for the different combination of datasets used in this work. We assume a flat prior in $\log_{10}\left( G_{\rm eff} {\rm MeV}^2\right)$ with range $[-5,0]$. We note that the bimodality of the posterior implies that it is difficult to choose a unique smoothing kernel that is valid over the whole prior range. The smoothing kernel used here is a compromise between under smoothing the main mode and over smoothing the interacting neutrino mode. To illustrate this latter effect, we show in the inset the interacting neutrino mode plotted using a much narrower smoothing kernel appropriate to the width of this mode.
• Figure 2: Posterior distributions for the cosmological parameters most affected by neutrino self-interaction. We illustrate here the constraints obtained by using Planck temperature-only data (red), as well as the combination of Planck temperature and E-mode polarization data (black). The contours in the two-dimensional plots give the 68% and 95% confidence regions.
• Figure 3: Similar to the posterior distributions shown in figure \ref{['fig:triang_base']}, but adding the BAO measurements from the SDSS BOSS DR12 alam16.
• Figure 4: Similar to the posterior distributions shown in figure \ref{['fig:triang_base']}, but adding the BAO measurements from the SDSS BOSS DR12 alam16 and the local measurement of the Hubble parameter from ref. riess11.
• Figure 5: Neutrino visibility function $g_\nu(\tau) = -\dot{\tau}_\nu e^{-\tau_\nu}$ as a function of conformal time $\tau$. The top $x$-axis shows the approximate CMB multipole $l_{\rm entry}$ that is entering the causal horizon at each value of $\tau$ according to the relation $l_{\rm entry} = 0.75(\tau_0/\tau)$Dodelson-Cosmology-2003, where $\tau_0$ is the conformal time today. The solid brown line shows a model where neutrino free streaming occurs early enough as to not affect the CMB, while the red dashed line displays the model which corresponds to the 95% upper bound on $G_{\rm eff}$ from the $\Lambda$CDM mode. The dot-dashed blue line shows the neutrino visibility function best fit from the interacting neutrino mode. The grayed region shows the approximate range of conformal time probed by the the CMB multipole $410<l<2500$, while the green region illustrates the range probed by the full width of the first CMB temperature peak ($50<l<410$).