PUB - Publikationen an der Universität Bielefeld

**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 ν_Hcouples to a lighter one ν_land a massless scalar particle ϕ 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 ν_H, ν_l, and ϕ 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 ν_His 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 Γ_T=(1/τ₀) (m_νH/E_νH)³, but at a rate ∼ (1/₀) (m_νH/E_νH)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 τ₀from τ₀^old≳ 1.2 × 10⁹s (m_νH/50 meV)³to τ₀≳ (4 × 10⁵→ 4 × 10⁶) s (m_νH/50 meV)⁵.