发表机构
Phenikaa Institute for Advanced Study, Phenikaa University（phenikaa大学先进研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
利用动力系统方法，首次确定Starobinsky-Grisaru-Zanon引力的精确de Sitter解，发现该解始终不稳定，且Starobinsky R²项虽不影响de Sitter解取值，但会影响其不稳定性。
AI 中文摘要
我们研究包含所谓Grisaru-Zanon项的新型四阶引力模型——Starobinsky-Grisaru-Zanon引力是否存在稳定的de Sitter解。首先，我们利用基于欧拉-拉格朗日方程的有效方法，推导出对应于空间平坦的Friedmann-Lemaitre-Robertson-Walker度规的Starobinsky-Grisaru-Zanon引力场方程。接着，我们首次确定了这些场方程的一个精确de Sitter解。最后，我们通过动力系统方法指出，所得的de Sitter解始终是不稳定的。值得注意的是，尽管Starobinsky R²项对所得de Sitter解的取值没有贡献，但它确实会影响该解的不稳定性。
英文摘要
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.
Comments17 pages, 1 figure. Accepted for publication in International Journal of Geometric Methods in Modern Physics
Journal refInt. J. Geom. Meth. Mod. Phys. (2026) 2650267
