Do observations prove that cosmological neutrinos are thermally distributed?

TL;DR

The paper investigates whether cosmological observations prove relic neutrinos are thermally distributed by allowing the first two moments of the neutrino distributions to vary in a Bayesian framework. It introduces a concrete non-thermal scenario from out-of-equilibrium decays of a light scalar that adds a peaked contribution to the neutrino phase-space, and explores how BBN, CMB, and LSS constrain this distortion via parameters like $N_{ m eff}$, $\omega_\nu$, and $m_0$. The results show current data can accommodate sizeable non-thermal distortions, with strong degeneracies between $N_{ m eff}$, neutrino mass, and dark matter density; BBN is particularly powerful in limiting non-thermal energy density at late times, while CMB+LSS alone cannot break all degeneracies. Forecasts with Planck+SDSS and with CMBPOL+LSST suggest improved constraints but still reveal a persistent degeneracy between non-thermal corrections and extra relativistic degrees of freedom, unless external inputs (e.g., direct mass measurements or BBN constraints) are used. Overall, the work emphasizes that, although a thermal relic neutrino distribution is favored for simplicity, current cosmological data do not exclude non-thermal distortions, and distinguishing them from extra light species will require complementary observations.

Abstract

It is usually assumed that relic neutrinos possess a Fermi-Dirac distribution, acquired during thermal equilibrium in the Early Universe. However, various mechanisms could introduce strong distortions in this distribution. We perform a Bayesian likelihood analysis including the first moments of the three active neutrino distributions as free parameters, and show that current cosmological observations of light element abundances, Cosmic Microwave Background (CMB) anisotropies and Large Scale Structures (LSS) are compatible with very large deviations from the standard picture. We also calculate the bounds on non-thermal distortions which can be expected from future observations, and stress that CMB and LSS data alone will not be sensitive enough in order to distinguish between non-thermal distortions in the neutrino sector and extra relativistic degrees of freedom. This degeneracy could be removed by additional constraints from primordial nucleosynthesis or independent neutrino mass scale measurements.

Figures (4)

• Figure 1: Differential number density of relic neutrinos as a function of the comoving momentum for the non-thermal spectrum in Equation (\ref{['NTspec']}). The parameters are $A=0.018$, $y_*=10.5$ and $\sigma=1$, which corresponds to $N_{\rm eff} \simeq 4$.
• Figure 2: The 1 $\sigma$ (thin lines) and 2 $\sigma$ (thick lines) BBN bounds on the $\Phi$ number density (normalized to $T_\nu^3$) versus mass $M$ in MeV. The regions above the contours would be in disagreement with the observed primordial abundances of $^4$He or D.
• Figure 3: Marginalized likelihood for the parameters of each model: $\Lambda$CDM+NT (black, solid), $\Lambda$CDM+R (red, dashed), or $\Lambda$CDM (blue, dotted). The independent basis parameters are included in the first ten plots only. The last two plots show the related parameters ($A$, $y_*$) for the non-thermal model.
• Figure 4: Two-dimensional likelihoods illustrating the main degeneracy affecting the $\Lambda$CDM+NT model (for the $\Lambda$CDM+R model the plots are extremely similar). This degeneracy correlates $N_{\rm eff}$ mainly with $\omega_{\rm dm}$ (top left) and $m_0$ (middle left), and to a smaller extent with $\theta$ (top right) and $n_s$ (middle right). We also show how $N_{\rm eff}$ is correlated with two related parameters: the age of the Universe (bottom left) and the Hubble parameter (bottom right). The solid curves refer to the 1-$\sigma$ and 2-$\sigma$ contours of the marginalized likelihood. For comparison, the average sample likelihood is shown in color levels.