Abstract: We present in this work a new calculation of the standard-model benchmark value for the effective number of neutrinos, N-eff(SM), that quantifies the cosmological neutrinoto-photon energy densities. The calculation takes into account neutrino flavour oscillations, finite-temperature effects in the quantum electrodynamics plasma to O(e(3)), where e is the elementary electric charge, and a full evaluation of the neutrino-neutrino collision integral. We provide furthermore a detailed assessment of the uncertainties in the benchmark N(eff)(SM )value, through testing the value's dependence on (i) optional approximate modelling of the weak collision integrals, (ii) measurement errors in the physical parameters of the weak sector, and (iii) numerical convergence, particularly in relation to momentum discretisation. Our new, recommended standard-model benchmark is N-eff(SM) 3.0440 +/- 0.0002, where the nominal uncertainty is attributed predominantly to errors incurred in the numerical solution procedure (vertical bar delta N-eff vertical bar similar to 10(-4)), augmented by measurement errors in the solar mixing angle sin(2) theta(12) (vertical bar delta N-eff vertical bar similar to 10(-4)).

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 firstorder 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(T) = (1/tau(0))( m(nu H)/E-nu H)(3), but at a rate similar to (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(old)(0) greater than or similar to 1.2 x 10(9) s (m(nu H)/50 meV)(3) to tau(0) greater than or similar to (4 x 10(5) -> 4 x 10(6)) s (m(nu H)/50 meV)(5).

Abstract: In the framework of a 3+1 scheme with an additional inert state, we consider the thermalisation of sterile neutrinos in the early Universe taking into account the full 4 x 4 mixing matrix. The evolution of the neutrino energy distributions is found solving the momentum-dependent kinetic equations with full diagonal collision terms, as in previous analyses of flavour neutrino decoupling in the standard case. The degree of thermalisation of the sterile state is shown in terms of the effective number of neutrinos, N-eff, and its dependence on the three additional mixing angles (theta(14), theta(24), theta(34)) and on the squared mass difference Delta m(41)(2) is discussed. Our results are relevant for fixing the contribution of a fourth light neutrino species to the cosmological energy density, whose value is very well constrained by the final Planck analysis. For the preferred region of active-sterile mixing parameters from short-baseline neutrino experiments, we find that the fourth state is fully thermalised (N-eff similar or equal to 4).