Stability issues of nonlocal gravity during primordial inflation

Abstract

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 $Δ_4$ models, previously introduced by our group. We find that the RR and $Δ_4$ 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.

v3: important error corrected, which changes a conclusion (RT model viable also when initial conditions are set during inflation); v4: corrected an error in the v3 submission (abstract in the arxiv form had not been changed)