Towards a complete scheme of cosmological neutrino self-interactions: Collision term for a wide range of mediator masses

Abstract

Neutrino self-interactions (NSI) offer a potential pathway to address anomalies in standard cosmology and explain existing cosmological tensions. In this work, we present a novel framework to obtain the neutrino--neutrino collision term within the Boltzmann hierarchy, incorporating both neutrino and mediator masses as free parameters. Our calculations encompass both Dirac-like and Majorana neutrinos and distinguish between two neutrino mass eigenstates. This work provides a valuable tool for future analyses, should a NSI signal be detected. Remarkably, our results show a smooth transition from the light to the heavy mediator approximation as the Universe cools down for non-resonant cases. Thus, for the widely studied heavy mediator, our new scheme eliminates the need to approximate at high redshifts when the temperature increases above the mediator mass, and it provides the tools to test the threshold of validity of the heavy mediator paradigm. While this work focuses on NSI mediated by a scalar particle, the presented framework could be adapted to a broader range of neutrino NSI and possibly to warm dark matter self-interacting scenarios.

Figures (7)

• Figure 1: Feynman diagrams at tree level involved in the scalar mediated $\nu_i\nu_j \rightarrow \nu_i\nu_j$ scattering with: a) s-channel (valid only for Majorana neutrinos and neutrino–antineutrino pairs), b) channel t, c) channel u (only valid for the same mass eigenstate).
• Figure 2: General scheme for computing the collision term in $2 \to 2$ scattering.
• Figure 3: Massive neutrino effects in the ${\cal K}_\ell(z_1)$ term for elastic scattering involving the same mass eigenstate and a massive mediator ($m_\varphi = 10^3\,\mathrm{eV}$): (a) $T_\nu = 1\,\mathrm{eV}$, (b) $T_\nu = 5\,\mathrm{eV}$. Solid lines correspond to $m_\nu=0$ and dotted lines to $m_\nu=0.1 {\rm eV}$. The percentage deviation with respect to the massless case is also shown for selected non-vanishing multipole contributions. The residual noise arises from the Monte Carlo integration performed with Vegas.
• Figure 4: Neutrino nature effects in the ${\cal K}_\ell(z_1)$-term in elastic scattering for same mass eigenstate, $m_\nu = 0.05 \, {\rm eV}$, where solid lines correspond for Dirac-like and dotted lines for Majorana neutrinos: (a) $T_\nu=1 \, {\rm eV}$, (b) $T_\nu=5 \, {\rm eV}$. The percentage deviation with respect to the Dirac-like case is also shown for selected non-vanishing multipole contributions. The residual noise arises from the Monte Carlo integration performed with Vegas.
• Figure 5: Relationship between temperature $T_\nu$ and mediator mass $m_\varphi$ for NSI with $\beta_\ell$ computation excluding resonance contribution: Majorana ($M$) vs Dirac-like ($D$) for $m_\varphi = 10^3 \, {\rm eV}$ at $\ell = 5$. In the blue curves, the effectively massless neutrino interacts with itself, while in the purple ones it interacts with another massive neutrino with $m_j=0.05\rm{eV}$.