Changing the Bayesian prior: Absolute neutrino mass constraints in nonlocal gravity

Prior change is discussed in observational constraints studies of nonlocally modified gravity, where a model characterized by a modification of the form m^2R^-2R to the Einstein-Hilbert action was compared against the base one in a Bayesian way. It was found that the competing modified gravity model is significantly disfavored (at 22: 1 in terms of betting-odds) against given CMB+SNIa+BAO data, because of a tension appearing in the H₀--₌ plane. We identify the underlying mechanism generating such a tension and show that it is mostly caused by the late-time, quite smooth, phantom nature of the effective dark energy described by the nonlocal model. We find that the tension is resolved by considering an extension of the initial baseline, consisting in allowing the absolute mass of three degenerated massive neutrino species m_/3 to take values within a prior interval consistent with existing data. As a net effect, the absolute neutrino mass is inferred to be nonvanishing at 2 level, best-fitting at m_0. 21 eV, and the Bayesian tension disappears rendering the nonlocal gravity model statistically equivalent to, given recent CMB+SNIa+BAO data. We also discuss constraints from growth rate measurements f₈, whose fit is found to be improved by a larger massive neutrino fraction as well. The -extended nonlocal model also prefers a higher value of H₀ than, therefore in better agreement with local measurements. Our study provides one more example suggesting that the neutrino density fraction _ is partially degenerated with the nature of the dark energy. This emphasizes the importance of cosmological and terrestrial neutrino research and, as a massive neutrino background impacts structure formation observables non-negligibly, proves to be especially relevant for future galaxy surveys.