Stability issues of nonlocal gravity during primordial inflation

TL;DR

This paper investigates the stability of three nonlocal gravity models during primordial inflation, finding that two models are stable and the third's apparent instability is negligible due to scale differences.

Contribution

The study provides a detailed analysis of the stability of RT, RR, and Δ4 nonlocal gravity models during inflation, demonstrating the viability of all three models in this regime.

Findings

RR and Δ4 models are stable during inflation.

RT model shows an apparent instability, but it is negligible.

All three models can have viable evolution 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 $\Delta_4$ 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.