Observational Constraints in Nonlocal Gravity: the Deser-Woodard Case

Understand

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 $\sim R f(\Box^{-1}R)$, where $f$ is a free function.

• Choosing $f$ so as to reproduce the $\Lambda{\rm CDM}$ 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 $\Lambda{\rm CDM}$, up to several percents.
• Such prominent growth and lensing features lead to the inference of a significantly smaller value of $\sigma_8$ with respect to the one in $\Lambda{\rm CDM}$, given \textit{Planck} CMB+lensing data.