Abstract: One of the most criticized features of Bayesian statistics is the fact that credible intervals, especially when open likelihoods are involved, may strongly depend on the prior shape and range. Many analyses involving open likelihoods are affected by the eternal dilemma of choosing between linear and logarithmic prior, and in particular in the latter case the situation is worsened by the dependence on the prior range under consideration. In this letter, we revive a simple method to obtain constraints that depend neither on the prior shape nor range and, using the tools of Bayesian model comparison, extend it to overcome the possible dependence of the bounds on the choice of free parameters in the numerical analysis. An application to the case of cosmological bounds on the sum of the neutrino masses is discussed as an example.

Abstract: In this manuscript we reassess the potential of interacting dark matter-dark energy models in solving the Hubble constant tension. These models have been proposed but also questioned as possible solutions to the H0 problem. Here we examine several interacting scenarios against cosmological observations, focusing on the important role played by the calibration of supernovae data. In order to reassess the ability of interacting dark matter-dark energy scenarios in easing the Hubble constant tension, we systematically confront their theoretical predictions using a prior on the supernovae Ia absolute magnitude MB, which has been argued to be more robust and certainly less controversial than using a prior on the Hubble constant H0. While some data combinations do not show any preference for interacting dark sectors and in some of these scenarios the clustering sigma 8 tension worsens, interacting cosmologies with a dark energy equation of state w < -1 are preferred over the canonical lambda CDM picture even with cosmic microwave background data alone and also provide values of sigma 8 in perfect agreement with those from weak lensing surveys. Future cosmological surveys will test these exotic dark energy cosmologies by accurately measuring the dark energy equation of state and its putative redshift evolution.

Abstract: We present robust, model-marginalized limits on both the total neutrino mass (E m1,) and abundances (Neff) to minimize the role of parametrizations, priors and models when extracting neutrino properties from cosmology. The cosmological observations we consider are cosmic microwave background temperature fluctuation and polarization measurements, supernovae Ia luminosity distances, baryon acoustic oscillation observations and determinations of the growth rate parameter from the Data Release 16 of the Sloan Digital Sky Survey IV. The degenerate neutrino mass spectrum (which implies the prior sigma m(1), > 0) is weakly or moderately preferred over the normal and inverted hierarchy possibilities, which imply the priors sigma m(1), > 0.06 and sigma m(1), > 0.1 eV respectively. Concerning the underlying cosmological model, the ACDM minimal scenario is almost always strongly preferred over the possible extensions explored here. The most constraining 95% CL bound on the total neutrino mass in the ACDM + sigma m(1), picture is sigma m(1), < 0.087 eV. The parameter N-eff is restricted to 3.08 +/- 0.17 (68% CL) in the ACDM + Neff model. These limits barely change when considering the ACDM + sigma m(1), + Neff scenario. Given the robustness and the strong constraining power of the cosmological measurements employed here, the model -marginalized posteriors obtained considering a large spectra of nonminimal cosmologies are very close to the previous bounds, obtained within the ACDM framework in the degenerate neutrino mass spectrum. Future cosmological measurements may improve the current Bayesian evidence favoring the degenerate neutrino mass spectra, challenging therefore the consistency between cosmological neutrino mass bounds and oscillation neutrino measurements, and potentially suggesting a more complicated cosmological model and/or neutrino sector.