Abstract: We present a novel approach to derive constraints on neutrino masses, as well as on other cosmological parameters, from cosmological data, while taking into account our ignorance of the neutrino mass ordering. We derive constraints from a combination of current as well as future cosmological datasets on the total neutrino mass M-nu and on the mass fractions f(nu),i = m(i)/M-nu (where the index i = 1, 2, 3 indicates the three mass eigenstates) carried by each of the mass eigenstates m(i), after marginalizing over the (unknown) neutrino mass ordering, either normal ordering (NH) or inverted ordering (IH). The bounds on all the cosmological parameters, including those on the total neutrino mass, take therefore into account the uncertainty related to our ignorance of the mass hierarchy that is actually realized in nature. This novel approach is carried out in the framework of Bayesian analysis of a typical hierarchical problem, where the distribution of the parameters of the model depends on further parameters, the hyperparameters. In this context, the choice of the neutrino mass ordering is modeled via the discrete hyperparameter h(type), which we introduce in the usual Markov chain analysis. The preference from cosmological data for either the NH or the IH scenarios is then simply encoded in the posterior distribution of the hyper-parameter itself. Current cosmic microwave background (CMB) measurements assign equal odds to the two hierarchies, and are thus unable to distinguish between them. However, after the addition of baryon acoustic oscillation (BAO) measurements, a weak preference for the normal hierarchical scenario appears, with odds of 4 : 3 from Planck temperature and large-scale polarization in combination with BAO (3 : 2 if small-scale polarization is also included). Concerning next-generation cosmological experiments, forecasts suggest that the combination of upcoming CMB (COrE) and BAO surveys (DESI) may determine the neutrino mass hierarchy at a high statistical significance if the mass is very close to the minimal value allowed by oscillation experiments, as for NH and a fiducial value of M-nu = 0.06 eV there is a 9 : 1 preference of normal versus inverted hierarchy. On the contrary, if the sum of the masses is of the order of 0.1 eV or larger, even future cosmological observations will be inconclusive. The innovative statistical strategy exploited here represents a very simple, efficient and robust tool to study the sensitivity of present and future cosmological data to the neutrino mass hierarchy, and a sound competitor to the standard Bayesian model comparison. The unbiased limit on M-nu we obtain is crucial for ongoing and planned neutrinoless double beta decay searches.

Abstract: We study the impact of assumptions about neutrino properties on the estimation of inflationary parameters from cosmological data, with a specific focus on the allowed contours in the n(s)/r plane, where n(s) is the scalar spectral index and r is the tensor-to-scalar ratio. We study the following neutrino properties: (i) the total neutrino mass M-i = Sigma(i)m(i) (where the index i = 1, 2, 3 runs over the three neutrino mass eigenstates); (ii) the number of relativistic degrees of freedom N-eff at the time of recombination; and (iii) the neutrino hierarchy. Whereas previous literature assumed three degenerate neutrino masses or two massless neutrino species (approximations that clearly do not match neutrino oscillation data), we study the cases of normal and inverted hierarchy. Our basic result is that these three neutrino properties induce < 1 sigma shift of the probability contours in the n(s)/r plane with both current or upcoming data. We find that the choice of neutrino hierarchy (normal, inverted, or degenerate) has a negligible impact. However, the minimal cutoff on the total neutrino mass M-v,M-min = 0 that accompanies previous works using the degenerate hierarchy does introduce biases in the n(s)/r plane and should be replaced by M-v,M-min = 0.059 eV as required by oscillation data. Using current cosmic microwave background (CMB) data from Planck and Bicep/Keck, marginalizing over the total neutrino mass M-v and over r can lead to a shift in the mean value of ns of similar to 0.3 sigma toward lower values. However, once baryon acoustic oscillation measurements are included, the standard contours in the n(s)/r plane are basically reproduced. Larger shifts of the contours in the n(s)/r plane (up to 0.8 sigma) arise for nonstandard values of N-eff. We also provide forecasts for the future CMB experiments Cosmic Origins Explorer (COrE, satellite) and Stage-IV (ground-based) and show that the incomplete knowledge of neutrino properties, taken into account by a marginalization over M-v, could induce a shift of similar to 0.4 sigma toward lower values in the determination of ns (or a similar to 0.8 sigma shift if one marginalizes over N-eff). Comparison to specific inflationary models is shown. Imperfect knowledge of neutrino properties must be taken into account properly, given the desired precision in determining whether or not inflationary models match the future data.

Abstract: We explore cosmological constraints on the sum of the three active neutrino masses M-v in the context of dynamical dark energy (DDE) models with equation of state (EoS) parametrized as a function of redshift z by w(z) = w(0) + w(a)z/ (1 + z), and satisfying w(z) >= -1 for all z. We make use of cosmic microwave background data from the Planck satellite, baryon acoustic oscillation measurements, and supernovae la luminosity distance measurements, and perform a Bayesian analysis. We show that, within these models, the bounds on M-v do not degrade with respect to those obtained in the Lambda CDM case; in fact, the bounds arc slightly tighter, despite the enlarged parameter space. We explain our results based on the observation that, for fixed choices of w(0), w(a) such that w(z) >= -1 (but not w = -1 for all z), the upper limit on M-v is tighter than the Lambda CDM limit because of the well-known degeneracy between w and M-v. The Bayesian analysis we have carried out then integrates over the possible values of w(0)-w(a) such that w(z) >= -1, all of which correspond to tighter limits on M-v than the Lambda CDM limit. We find a 95% credible interval (C.I.) upper bound of M-v < 0.13 eV. This bound can be compared with the 95% C.I. upper bounds of M-v < 0.16 eV, obtained within the Lambda CDM model, and M-v < 0.41 eV, obtained in a DDE model with arbitrary EoS (which allows values of w < -1). Contrary to the results derived for DDE models with arbitrary EoS, we find that a dark energy component with w(z) >= -1 is unable to alleviate the tension between high-redshift observables and direct measurements of the Hubble constant H o . Finally, in light of the results of this analysis, we also discuss the implications for DDE models of a possible determination of the neutrino mass ordering by laboratory searches.