Neutrino-neutrino interactions can lead to collective flavour conversion effects in supernovae and in the early universe. We demonstrate that the case of "bipolar" oscillations, where a dense gas of neutrinos and antineutrinos in equal numbers completely converts from one flavour to another even if the mixing angle is small, is equivalent to a pendulum in flavour space. Bipolar flavour conversion corresponds to the swinging of the pendulum, which begins in an unstable upright position (the initial flavour), and passes through momentarily the vertically downward position (the other flavour) in the course of its motion. The time scale to complete one cycle of oscillation depends logarithmically on the vacuum mixing angle. Likewise, the presence of an ordinary medium can be shown analytically to contribute to a logarithmic increase in the bipolar conversion period. We further find that a more complex (and realistic) system of unequal numbers of neutrinos and antineutrinos is analogous to a spinning top subject to a torque. This analogy easily explains how such a system can oscillate in both the bipolar and the synchronised mode, depending on the neutrino density and the size of the neutrino-antineutrino asymmetry. Our simple model applies strictly only to isotropic neutrino gasses. In more general cases, and especially for neutrinos streaming from a supernova core, different modes couple to each other with unequal strength, an effect that can lead to kinematical decoherence in flavour space rather than collective oscillations. The exact circumstances under which collective oscillations occur in non-isotropic media remain to be understood.

Abstract. The Fisher matrix formalism has in recent times become the standard method for predicting the precision with which various cosmological parameters can be extracted from future data. This approach is fast, and generally returns accurate estimates for the parameter errors when the individual parameter likelihoods approximate a Gaussian distribution. However, where Gaussianity is not respected (due, for instance, to strong parameter degeneracies), the Fisher matrix formalism loses its reliability. In this paper, we compare the results of the Fisher matrix approach with those from Monte Carlo simulations. The latter method is based on the publicly available CosmoMC code, but uses synthetic realisations of data sets anticipated for future experiments. We focus on prospective cosmic microwave background (CMB) data from the Planck satellite, with or without CMB lensing information, and its implications for a minimal cosmological scenario with eight parameters and an extended model with eleven parameters. We show that in many cases, the projected sensitivities from the Fisher matrix and the Monte Carlo methods differ significantly, particularly in models with many parameters. Sensitivities to the neutrino mass and the dark matter fraction are especially susceptible to change.

Abstract. We study the gravitational clustering of big bang relic neutrinos onto existing cold dark matter (CDM) and baryonic structures within the flat ΛCDM model, using both numerical simulations and a semi-analytical linear technique, with the aim of understanding the neutrinos' clustering properties for direct detection purposes. In a comparative analysis, we find that the linear technique systematically underestimates the amount of clustering for a wide range of CDM halo and neutrino masses. This invalidates earlier claims of the technique's applicability. We then compute the approximate phase space distribution of relic neutrinos in our neighbourhood at Earth, and estimate the large scale neutrino density contrasts within the local Greisen-Zatsepin-Kuzmin zone. With these findings, we discuss the implications of gravitational neutrino clustering for scattering-based detection methods, ranging from flux detection via Cavendish-type torsion balances, to target detection using accelerator beams and cosmic rays. For emission spectroscopy via resonant annihilation of extremely energetic cosmic neutrinos on the relic neutrino background, we give new estimates for the expected enhancement in the event rates in the direction of the Virgo cluster.

Neutrino-neutrino interactions can lead to collective flavour conversion effects in supernovae and in the early universe. We demonstrate that the case of "bipolar" oscillations, where a dense gas of neutrinos and antineutrinos in equal numbers completely converts from one flavour to another even if the mixing angle is small, is equivalent to a pendulum in flavour space. Bipolar flavour conversion corresponds to the swinging of the pendulum, which begins in an unstable upright position (the initial flavour), and passes through momentarily the vertically downward position (the other flavour) in the course of its motion. The time scale to complete one cycle of oscillation depends logarithmically on the vacuum mixing angle. Likewise, the presence of an ordinary medium can be shown analytically to contribute to a logarithmic increase in the bipolar conversion period. We further find that a more complex (and realistic) system of unequal numbers of neutrinos and antineutrinos is analogous to a spinning top subject to a torque. This analogy easily explains how such a system can oscillate in both the bipolar and the synchronised mode, depending on the neutrino density and the size of the neutrino-antineutrino asymmetry. Our simple model applies strictly only to isotropic neutrino gasses. In more general cases, and especially for neutrinos streaming from a supernova core, different modes couple to each other with unequal strength, an effect that can lead to kinematical decoherence in flavour space rather than collective oscillations. The exact circumstances under which collective oscillations occur in non-isotropic media remain to be understood.

We study cosmological models that contain sterile neutrinos with eV-range masses as suggested by reactor and short-baseline oscillation data. We confront these models with both precision cosmological data (probing the CMB decoupling epoch) and light-element abundances (probing the BBN epoch). In the minimal ΛCDM model, such sterile neutrinos are strongly disfavoured by current data because they contribute too much hot dark matter. However, if the cosmological framework is extended to include also additional relativistic degrees of freedom beyond the three standard neutrinos and the putative sterile neutrinos, then the hot dark matter constraint on the sterile states is considerably relaxed. A further improvement is achieved by allowing a dark energy equation of state parameter w < −1. While BBN strongly disfavours extra radiation beyond the assumed eV-mass sterile neutrino, this constraint can be circumvented by a small ν e degeneracy. Any model containing eV-mass sterile neutrinos implies also strong modifications of other cosmological parameters. Notably, the inferred cold dark matter density can shift up by 20-75% relative to the standard ΛCDM value.