On the ghost-induced instability on de Sitter background

TL;DR

This paper investigates how rapid cosmic expansion during inflation suppresses ghost-induced instabilities in tensor perturbations of higher derivative gravity, even at trans-Planckian frequencies, contrasting with stability conditions in milder backgrounds.

Contribution

It demonstrates that a large Hubble rate during inflation can suppress tensor instabilities at high frequencies, extending understanding of stability in higher derivative gravity models.

Findings

Rapid expansion suppresses ghost-induced instabilities at high frequencies.

Instability is mitigated in de Sitter backgrounds with large Hubble rates.

High-frequency gravitational waves remain stable during inflation.

Abstract

It is known that the perturbative instability of tensor excitations in higher derivative gravity may not take place if the initial frequency of the gravitational waves are below the Planck threshold. One can assume that this is a natural requirement if the cosmological background is sufficiently mild, since in this case the situation is qualitatively close to the free gravitational wave in flat space. Here, we explore the opposite situation and consider the effect of a very far from Minkowski radiation-dominated or de Sitter cosmological background with a large Hubble rate, e.g., typical of an inflationary period. It turns out that, then, for initial Planckian or even trans-Planckian frequencies, the instability is rapidly suppressed by the very fast expansion of the universe.