Invisible neutrino decay in precision cosmology

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 $\varphi$ 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 $\varphi$ 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 ${\Gamma }_{\mathrm{T}}=(1/{\tau }_0)(m_{\nu H}/E_{\nu H}{)}^3$, 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 ${\tau }_0^{\mathrm{old}}\gtrsim 1.2\times 10^9\mathrm{s}(m_{\nu H}/50\mathrm{meV}{)}^3$ to ${\tau }_0\gtrsim (4\times 10^5\to 4\times 10^6)\mathrm{s}(m_{\nu H}/50\mathrm{meV}{)}^5$.

53 pages, 10 figures, v2 matches the accepted JCAP version

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