Weaker yet again: mass spectrum-consistent cosmological constraints on the neutrino lifetime

Understand

We consider invisible neutrino decay $\nu_H \to \nu_l + \phi$ in the ultra-relativistic limit and compute the neutrino anisotropy loss rate relevant for the cosmic microwave background (CMB) anisotropies.

• Improving on our previous work which assumed massless $\nu_l$ and $\phi$, we reinstate in this work the daughter neutrino mass $m_{\nu l}$ in a manner consistent with the experimentally determined neutrino mass splittings.
• We find that a nonzero $m_{\nu l}$ introduces a new phase space factor in the loss rate $\Gamma_{\rm T}$ proportional to $(\Delta m_\nu^2/m_{\nu_H}^2)^2$ in the limit of a small squared mass gap between the parent and daughter neutrinos, i.e., $\Gamma_{\rm T} \sim (\Delta m_\nu^2/m_{\nu H}^2)^2 (m_{\nu H}/E_\nu )^5 (1/\tau_0)$, where $\tau_0$ is the $\nu_H$ rest-frame lifetime.
• Using a general form of this result, we update the limit on $\tau_0$ using the Planck 2018 CMB data.