Non-local gravity and comparison with observational datasets. II. Updated results and Bayesian model comparison with $Λ$CDM

We present a comprehensive and updated comparison with cosmological observations of two non-local modifications of gravity previously introduced by our group, the so called RR and RT models. We implement the background evolution and the cosmological perturbations of the models in a modified Boltzmann code, using CLASS. We then test the non-local models against the {\em Planck} 2015 TT, TE, EE and Cosmic Microwave Background (CMB) lensing data, isotropic and anisotropic Baryonic Acoustic Oscillations (BAO) data, JLA supernovae, $H_0$ measurements and growth rate data, and we perform Bayesian parameter estimation. We then compare the RR, RT and $Λ$CDM models, using the Savage-Dickey method. We find that the RT model and $Λ$CDM perform equally well, while the performance of the RR model with respect to $Λ$CDM depends on whether or not we include a prior on $H_0$ based on local measurements.

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