Observational constraints in nonlocal gravity: the Deser-Woodard case

We study the cosmology of a specific class of nonlocal model of modified gravity, the so-called Deser-Woodard (DW) model, modifying the Einstein-Hilbert action by a term ~ R f(−1R), where f is a free function. Choosing f so as to reproduce the ΛCDM cosmological background expansion history within the nonlocal model, we implement the model in a cosmological linear Einstein-Boltzmann solver and study the deviations to GR the model induces in the scalar and tensor perturbations. We observe that the DW nonlocal model describes a modified propagation for the gravitational waves, as well as a lower linear growth rate and a stronger lensing power as compared to ΛCDM, up to several percents. Such prominent growth and lensing features lead to the inference of a significantly smaller value of σ8 with respect to the one in ΛCDM, given Planck CMB+lensing data. The prediction for the linear growth rate fσ8 within the DW model is therefore significantly smaller than the one in ΛCDM and the addition of growth rate data fσ8 from Redshift-space distortion measurements to Planck CMB+lensing, opens a (dominant) tension between Redshift-space distortion data and the reconstructed Planck CMB lensing potential. However, model selection issues only result in "weak" evidences for ΛCDM against the DW model given the data. Such a fact shows that the joined datasets we consider are not constraining enough for distinguishing between the models on firm grounds. As we discuss, the addition of galaxy WL data or the consideration of cosmological constraints from future galaxy clustering, weak lensing surveys, but also third generation gravitational wave interferometers, prove to be useful for discriminating modified gravity models such as the DW one from ΛCDM, within the close future.