Primordial high energy neutrinos: theoretical/observational constraints and sharp spectral features

Among the few ways that allow or could allow us to probe the early Universe from the observation of a flux of primordial particles, there is one possibility which has been little studied: the observation today of high energy neutrinos which could have been emitted shortly after the Big Bang, from the decay or annihilation of early universe relics. We perform a general study of such a possibility. To this end, we first emphasise that these neutrinos could display various kinds of sharp spectral features, resulting from the primary energy spectrum at emission, and from how this spectrum is smoothed by redshift and radiative correction effects. Next, we determine the ranges of mass (from a fraction of eV all the way to the Planck scale) and lifetime of the source particles along which we do not/we do expect that the sharp spectral feature will be altered by interactions of the neutrinos on their way to the detector, mainly with the cosmic neutrino background or between themselves. We also study the theoretical (i.e. mainly BBN and CMB) and observational constraints which hold on such a possibility. This allows us to delineate the regions of parameter space (mass, lifetime and abundance) that are already excluded, hopeless for future observation or, instead, which could lead to the observation of such neutrinos in the near future.