Non-local gravity and comparison with observational datasets

We study the cosmological predictions of two recently proposed non-local modifications of General Relativity. Both models have the same number of parameters as ACDM, with a mass parameter m replacing the cosmological constant. We implement the cosmological perturbations of the non-local models into a modification of the CLASS Boltzmann code, and we make a full comparison to CMB, BAO and supernova data. We find that the non-local models fit these datasets very well, at the same level as ACDM. Among the vast literature on modified gravity models, this is, to our knowledge, the only example which fits data as well as ACDM without requiring any additional parameter. For both non-local models parameter estimation using Planck+JLA+BAO data gives a value of Ho slightly higher than in ACDM.