Invisible neutrino decay in precision cosmology

TL;DR

This paper develops a first-principles approach to modeling invisible neutrino decay in cosmology, revealing key theoretical issues and revising constraints on neutrino lifetimes based on decay dynamics.

Contribution

It derives complete Boltzmann equations for neutrino-scalar systems and uncovers fundamental violations in existing models, leading to revised cosmological bounds on neutrino decay lifetimes.

Findings

Existing models violate momentum conservation and gauge invariance in the non-relativistic limit.

Exponential damping occurs at a rate proportional to (m/E)^5, not (m/E)^3 as previously assumed.

Revised lower bounds on neutrino lifetime are significantly less restrictive.

Abstract

We revisit the topic of invisible neutrino decay in the precision cosmological context, via a first-principles approach to understanding the cosmic microwave background and large-scale structure phenomenology of such a non-standard physics scenario. Assuming an effective Lagrangian in which a heavier standard-model neutrino $\nu_H$ couples to a lighter one $\nu_l$ and a massless scalar particle $\phi$ via a Yukawa interaction, we derive from first principles the complete set of Boltzmann equations, at both the spatially homogeneous and the first-order inhomogeneous levels, for the phase space densities of $\nu_H$, $\nu_l$, and $\phi$ in the presence of the relevant decay and inverse decay processes. With this set of equations in hand, we perform a critical survey of recent works on cosmological invisible neutrino decay in both limits of decay while $\nu_H$ is ultra-relativistic and non-relativistic. Our two main findings are: (i) in the non-relativistic limit, the effective equations of motion used to describe perturbations in the neutrino--scalar system in the existing literature formally violate momentum conservation and gauge invariance, and (ii) in the ultra-relativistic limit, exponential damping of the anisotropic stress does not occur at the commonly-used rate $\Gamma_{\rm T} =(1/\tau_0) (m_{\nu H}/E_{\nu H})^3$, but at a rate $\sim (1/\tau_0) (m_{\nu H}/E_{\nu H})^5$. Both results are model-independent. The impact of the former finding on the cosmology of invisible neutrino decay is likely small. The latter, however, implies a significant revision of the cosmological limit on the neutrino lifetime $\tau_0$ from $\tau_0^{\rm old} \gtrsim 1.2 \times 10^9\, {\rm s}\, (m_{\nu H}/50\, {\rm meV})^3$ to $\tau_0 \gtrsim (4 \times 10^5 \to 4 \times 10^6)\, {\rm s}\, (m_{\nu H}/50 \, {\rm meV})^5$.