Stability issues of nonlocal gravity during primordial inflation

We study the cosmological evolution of some nonlocal gravity models, when the initial conditions are set during a phase of primordial inflation. We examine in particular three models, the so-called RT, RR and Δ4 models, previously introduced by our group. We find that, during inflation, the RT model has a viable background evolution but at the level of cosmological perturbations develops instabilities, that make it non-viable. In contrast, the RR and Δ4 models have a viable evolution also when their initial conditions are set during a phase of primordial inflation.