Stability analysis of de Sitter solution in the Starobinsky-Grisaru-Zanon gravity using the dynamical system method
Abstract
We study whether the so-called Starobinsky-Grisaru-Zanon gravity, which is a novel fourth-order gravity model involving the so-called Grisaru-Zanon term, admits a stable de Sitter solution. First, we derive the corresponding field equations of the Starobinsky-Grisaru-Zanon gravity for the spatially flat Friedmann-Lemaitre-Robertson-Walker metric by using an effective method based on the Euler-Lagrange equations. Then, we figure out an exact de Sitter solution of these field equations for the first time. Finally, we point out, through the dynamical system method, that the obtained de Sitter solution is always unstable. Interestingly, although the Starobinsky R2 term does not contribute to the value of the obtained de Sitter solution, it does affect on the instability of this solution.
Versions
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BibTeX
@misc{do2026stability,
title = {{Stability analysis of de Sitter solution in the Starobinsky-Grisaru-Zanon gravity using the dynamical system method}},
author = {Tuan Q. Do},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.04233},
eprint = {2609.04233},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.04233},
}
RIS
TY - UNPB
TI - Stability analysis of de Sitter solution in the Starobinsky-Grisaru-Zanon gravity using the dynamical system method
AU - Tuan Q. Do
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.04233
UR - https://arxiv.org/abs/2609.04233
AB - We study whether the so-called Starobinsky-Grisaru-Zanon gravity, which is a novel fourth-order gravity model involving the so-called Grisaru-Zanon term, admits a stable de Sitter solution. First, we derive the corresponding field equations of the Starobinsky-Grisaru-Zanon gravity for the spatially flat Friedmann-Lemaitre-Robertson-Walker metric by using an effective method based on the Euler-Lagrange equations. Then, we figure out an exact de Sitter solution of these field equations for the first time. Finally, we point out, through the dynamical system method, that the obtained de Sitter solution is always unstable. Interestingly, although the Starobinsky R^2 term does not contribute to the value of the obtained de Sitter solution, it does affect on the instability of this solution.
ER -