Prior change is discussed in observational constraints studies of nonlocally modified gravity , where 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 tension appearing in the H _ { 0 } – \Omega _ { M } 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 \sum m _ { \nu } / 3 to take values within a prior interval consistent with existing data .
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 { 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 .
Our study provides one more example suggesting that the neutrino density fraction \Omega _ { \nu } 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 .