AI 中文总结
研究六阶引力中德西特暴胀解，通过推导场方程求解出解，发现系数$\gamma_1$和$\gamma_2$影响解的稳定性，当$3\gamma_1+\gamma_2 <0$时解不稳定，还研究了特殊极限情况，表明六阶引力更适合早期宇宙暴胀，二阶极限能给出稳定解。
AI 中文摘要
本文研究了一种六阶引力，它不仅包含两个主要项，即$\gamma_1 R\Box R$和$\gamma_2 R_{\mu\nu} \Box R^{\mu\nu}$，还包含二次曲率项和三次曲率项，以探究其是否存在精确的稳定德西特解。首先，在均匀各向同性的弗里德曼-勒梅特-罗伯逊-沃克背景时空下，基于欧拉-拉格朗日方程的有效方法推导六阶微分场方程。然后，解析求解这些场方程得到精确的德西特解，发现两个系数$\gamma_1$和$\gamma_2$虽不影响解的值，但影响其稳定性，当$3\gamma_1+\gamma_2 <0$时德西特解不稳定，通过数值计算验证了这一点。还研究了该引力模型的两个特殊极限情况。结果表明六阶引力更适合早期宇宙的暴胀阶段，只有二阶极限能给出与晚期宇宙加速膨胀兼容且稳定的德西特解。
英文摘要
A sixth-order gravity, which involves not only two leading terms, $γ_1 R\Box R$ and $γ_2 R_{μν} \Box R^{μν}$, but also quadratic curvature terms along with cubic curvature ones, will be investigated in this paper to see if it admits an exact stable de Sitter solution. First, we will derive sixth-order differential field equations of this gravity under the homogeneous and isotropic Friedmann-Lemaitre-Robertson-Walker background spacetime, using the effective method based on the Euler-Lagrange equations. Then, we will analytically solve these field equations to figure out an exact de Sitter solution, which turns out to be equivalent to a fixed point of the corresponding dynamical system of the studied gravity. Interestingly, two coefficients, $γ_1$ and $γ_2$, do not contribute to the value of the obtained de Sitter solution. However, they affect on the stability of the de Sitter solution. In particular, if these two coefficients obey the following inequality, $3γ_1+γ_2 <0$, then the de Sitter solution will always be unstable. Furthermore, numerical calculations will be performed to verify that the de Sitter fixed point is indeed a repeller of the dynamical system once this inequality is satisfied. All these results indicate that the sixth-order gravity is more suitable for an inflationary phase of early universe. To be complete, two special limits of the studied gravity model, in which field equations are reduced to second-order and fourth-order, respectively, will be investigated. As expected, only the second-order limit can always give raise a stable de Sitter solution, compatible with an accelerated expansion of late-time universe.
Comments21 pages, 3 figures. Comments are welcome
