Cosmology-marginalized approaches in Bayesian model comparison: The neutrino mass as a case study

Abstract

We propose here a novel method which singles out the a priori unavoidable dependence on the underlying cosmological model when extracting parameter constraints, providing robust limits which only depend on the considered dataset. Interestingly, when dealing with several possible cosmologies and interpreting the Bayesian preference in terms of the Gaussian statistical evidence, the preferred model is much less favored than when only two cases are compared. As a working example, we apply our approach to the cosmological neutrino mass bounds, which play a fundamental role not only in establishing the contribution of relic neutrinos to the dark matter of the Universe, but also in the planning of future experimental searches of the neutrino character and of the neutrino mass ordering.

Neutrino physics with the PTOLEMY project: active neutrino properties and the light sterile case

“…The absolute neutrino mass scale is still an unknown parameter, though cosmological observations and present results from tritium decay constrain the sum of the neutrino masses to be less than 0.12 − 0.6 [6,33,34,40] or 6 eV [17], respectively. The KATRIN experiment is expected to provide a limit which enters into the region for the neutrino mass that is still marginally allowed by cosmology.…”

Constraints on inflation with an extended neutrino sector

“…One of the most famous examples thereof is the constraint on the sum of neutrino masses from measurements of the CMB in combinations with Baryonic Acoustic Oscillations (BAO), m ν < 0.12 eV (95% CL) [15,16]. This bound depends on the assumed cosmological model [17] and in partcular can be relaxed if the average momentum of the CMB neutrinos is larger than that of a perfectly thermal distribution [18]. Additionally, it has been demonstrated in [2-4, 19, 20] that the CMB can also constrain models of non-standard neutrino interactions, like the Majoron models described in the previous section.…”

Constraining power of open likelihoods, made prior-independent

“…The situation is slightly different when more models are considered, for example if one wants to study and take into account several extensions of the same minimal scenario, as in Ref. [27]. It is not difficult to rewrite the definition of R to deal with multiple models, if we assume that the prior for the parameter x under consideration is the same in all of them, i.e.…”

“…that π(x) ≡ π(x|M i ) does not depend on M i . Let us now recall the method proposed in [27]. The modelmarginalized posterior distribution of the parameter x is obtained as…”

“…From the computational point of view, in the modelmarginalized case obtaining R is as simple as when only one model is considered. One just has to select a prior π(x) and a sufficiently broad range, obtain the marginalized posterior probability as in [27], then divide it by the considered prior and normalize appropriately.…”