Cosmological constraints on neutrino self-interactions with a light mediator

TL;DR

The study tests the cosmological impact of secret neutrino self-interactions mediated by a very light boson, using Planck 2015 CMB data to bound the effective coupling g_eff^4 that governs ν–ν scattering. By incorporating a relaxation-time collision term into the neutrino Boltzmann hierarchy and exploring one- and two-parameter extensions of ΛCDM, the authors derive upper limits on g_eff^4 (≈1.7×10^−27 at 95% C.I. with TTTEEE) and translate these into recoupling redshifts z_νrec, showing neutrinos remain free-streaming until near matter–radiation equality. A mild preference for nonzero g_eff^4 arises when high-ℓ polarization is included, though overall evidence remains conservative and robust against model extensions. The paper further connects these cosmological bounds to particle-physics scenarios, notably Majoron models, yielding g ≲ 7×10^−7 and v_σ ≳ 1.4×10^6 mν, and discusses implications for resolving cosmological tensions and for future data sensitivity.

Abstract

If active neutrinos undergo non-standard (`secret') interactions (NS$ν$I) the cosmological evolution of the neutrino fluid might be altered, leaving an imprint in cosmological observables. We use the latest publicly available CMB data from Planck to constrain NS$ν$I inducing $ν-ν$ scattering, under the assumption that the mediator $φ$ of the secret interaction is very light. We find that the effective coupling constant of the interaction, $g_\mathrm{eff}^4 \equiv \langle σv\rangle T_ν^2$, is constrained at $< 2.35\times10^{-27}$ (95\% credible interval), which stregthens to $g_\mathrm{eff}^4 < 1.64\times10^{-27}$ when Planck non-baseline small-scale polarization is considered. Our findings imply that after decoupling at $T\simeq 1$ MeV, cosmic neutrinos are free streaming at redshifts $z>3800$, or $z>2300$ if small-scale polarization is included. These bounds are only marginally improved when data from geometrical expansion probes are included in the analysis to complement Planck. We also find that the tensions between CMB and low-redshift measurements of the expansion rate $H_0$ and the amplitude of matter fluctuations $σ_8$ are not significantly reduced. Our results are independent on the underlying particle physics model as long as $φ$ is very light. Considering a model with Majorana neutrinos and a pseudoscalar mediator we find that the coupling constant $g$ of the secret interaction is constrained at $\lesssim 7\times 10^{-7}$. By further assuming that the pseudoscalar interaction comes from a dynamical realization of the see-saw mechanism, as in Majoron models, we can bound the scale of lepton number breaking $v_σ$ as $\gtrsim (1.4\times 10^{6})m_ν$.

Figures (6)

• Figure 1: Neutrino collision rate $\Gamma$ in units of the expansion rate $H$. The solid lines are drawn considering the total collision rate, i.e. for both weak processes and $\phi$-mediated interactions, and correspond to $g=\{1,\,2,\,3\}\times 10^{-7}$ from bottom to top. We also show the usual weak collision rate (purple long dashed line) and the $\phi$-mediated collision rate for $g = 1 \times 10^{-7}$ (red short dashed line). The gray band shows the region in which the collision rate is larger than the Hubble rate.
• Figure 2: Theoretical temperature APS for the $\Lambda \mathrm{CDM}$+$g_{\rm{eff}}$ model. Note that we are plotting $\ell^2{\mathcal{D}}_\ell = \ell^3 (\ell+1) C_\ell/2\pi$ to highlight changes at the high multipoles. In the upper panel we show the APS for three different values of the coupling constant, $g_{\rm{eff}}=\{2,\,3,\,4\} \times 10^{-7}$ (red dashed, cyan dotted, orange dotted curves, respectively). The blue points with error bars are the 2015 Planck data, and the black solid line is the $\Lambda \mathrm{CDM}$ best-fit ${\mathcal{D}}^{(0)}_\ell$ to the same data. In the middle panel we plot the differences with respect to $\Lambda \mathrm{CDM}$, $\Delta(\ell^2{\mathcal{D}}_\ell) = \ell^2({\mathcal{D}}_\ell-{\mathcal{D}}^{(0)}_\ell)$. The bottom panel shows the relative difference $\Delta {\mathcal{D}}_\ell/{\mathcal{D}}^{(0)}_\ell$.
• Figure 3: Same as Fig. \ref{['FIG:pws']}, but for the cross correlation between temperature and $E$-polarization. Note that in this case we do not show relative differences, since these diverge in some points due to the reference spectrum crossing zero.
• Figure 4: One-dimensional posterior probability for the effective parameter $g^4_\mathrm{eff}$ that characterizes the strength of neutrino-neutrino coupling, in the $\Lambda \mathrm{CDM}+g_\mathrm{eff}$ model. The blue (red) curves are obtained using $\mathsf{Planck_{15}TT}$ ($\mathsf{Planck_{15}TTTEEE}$) as the baseline CMB dataset. In the top panel these are the only data considered; in the two lower panels we also add information from external astrophysical datsets [$\mathsf{Planck_{15}TT(TTTEEE)}+$ext, middle panel] or lensing estimates from the CMB 4-point correlation function [$\mathsf{Planck_{15}TT(TTTEEE)}+$lensing, bottom panel]. See text for a more detailed description of the datasets. The shaded areas show 68% credible intervals.
• Figure 5: One-dimensional marginalized posterior distributions of the base $\Lambda \mathrm{CDM}$ parameters from $\mathsf{Planck_{15}TT}$, for the $\Lambda \mathrm{CDM}$ (black) and $\Lambda \mathrm{CDM}$$+g_{\rm{eff}}$ (red) models.