Inferencing neutrino mass hierarchy from cosmology
The observation of solar and atmospheric neutrino oscillations place bounds on the mass differences. However, these probes are insensitive to the absolute mass. To date, cosmology has provided the best bounds on the total neutrino mass. These bounds are based on a degenerate mass model. With the increasing precision of cosmological data, we investigate the effect of the neutrino mass hierarchy. The precision of the parameter estimates stems from precise observations of the cosmic microwave background. However, the effect of neutrino mass hierarchy on this observation is smaller than the cosmic variance. Therefore, we rely on the measurement of the matter power spectrum for hierarchy effects. We propose the use of importance sampling rather than the commonly used Markov chain Monte Carlo. Importance sampling takes advantage of the microwave background's statistical insensitivity to hierarchy. We present forecasted bounds due to Planck and the proposed CMBPol. We also discuss the needed precision for future galaxy surveys in detecting the effect of neutrino mass hierarchy.