Changing the prior: absolute neutrino mass constraints in nonlocal gravity

Prior change is discussed in observational constraints studies of nonlocally modified gravity. In the latter, a model characterized by a modification of the form $\sim m^2 R\Box^{-2}R$ to the Einstein-Hilbert action was compared against the base $\Lambda$CDM 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 $\Lambda$CDM given CMB+SNIa+BAO data, because of a dominant tension appearing in the $H_0 \,$-$\, \Omega_M$ plan. 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 possible solutions for it to be resolved and explore a given one that consists in extending the initial baseline from one massive neutrino eigenstate to three degenerate ones, whose absolute mass $\sum m_\nu \, / \, 3$ is allowed to take values within a reasonable prior interval. As a net effect, the absolute neutrino mass is inferred to be non-vanishing at $2 \sigma$ level, best-fitting at $\sum m_\nu \approx 0.21 {\, \rm eV}$, and the Bayesian tension disappears rendering the nonlocal gravity model statistically equivalent to $\Lambda$CDM, given recent CMB+SNIa+BAO data. We also discuss constraints from growth rate measurements $f \sigma_8$ whose fit is found to be improved by a larger massive neutrino fraction as well. The $\nu$-extended nonlocal model also prefers a higher value of $H_0$ than $\Lambda$CDM, therefore in better agreement with local measurements.