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 $\Delta_4$ models, previously introduced by our group. We find that the RR and $\Delta_4$ models have a stable evolution also during inflation. The RT model has an apparent instability, but we show that, because of the smallness of the scale associated to the nonlocal term compared to the inflationary scale, this instability is innocuous and also the RT model has a viable evolution even when its initial conditions are set during a phase of primordial inflation.