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 $\mathrm{\Lambda }$CDM, 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 as well as $\mathrm{\Lambda }$CDM. For both non-local models parameter estimation using Planck+JLA+BAO data gives a value of $H_0$ higher than in $\mathrm{\Lambda }$CDM, and in better agreement with the values obtained from local measurements.