Invisible neutrino decay in precision cosmology
Gabriela Barenboim, Joe Zhiyu Chen, Steen Hannestad, Isabel M. Oldengott, Thomas Tram, Yvonne Y.Y. Wong
Abstract
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 H couples to a lighter one ν l and 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 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 Γ T =(1/τ 0 ) (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 τ 0 from τ 0 old ≳ 1.2 × 10 9 s (m νH /50 meV) 3 to τ 0 ≳ (4 × 10 5 → 4 × 10 6 ) s (m νH /50 meV) 5 .