Stability analysis of de Sitter solution in the Einstein-Grisaru-Zanon gravity using the dynamical system method

Abstract

In this paper, we would like to investigate the stability of de Sitter solution in the Einstein-Grisaru-Zanon gravity, which is a novel fourth-order gravity model considered recently in a paper [Phys. Lett. B {\bf 855} (2024) 138811]. As a result, we are able to derive the corresponding field equations for the Einstein-Grisaru-Zanon gravity by using an effective method based on the Euler-Lagrange equations. Unfortunately, one of the obtained field equations does not coincide with that derived in the original paper of the Einstein-Grisaru-Zanon gravity due to a gap between higher-order derivative terms. However, our de Sitter solution is still identical to one solved in the original paper of the Einstein-Grisaru-Zanon gravity due to the vanishing of the gap. Furthermore, a stability analysis based on the dynamical system method is performed to indicate that the obtained de Sitter solution is always unstable, no matter it presents an inflationary phase or expanding phase of universe. This result confirms the validity of stability investigation carried out in the original paper of the Einstein-Grisaru-Zanon gravity.