发表机构
Universidad de La Frontera; Birla Institute of Technology and Science-Pilani, Hyderabad Campus; Universidad Católica del Norte; Pontificia Universidad Católica de Valparaíso（拉弗龙特拉大学; 比拉理工学院皮拉尼分校海德拉巴校区; 北方天主教大学; 瓦爾帕萊索天主教大學）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究二次F(R,G)宇宙学中均匀曲率模的稳定性，发现低曲率尘埃分支与de Sitter解，并给出稳定条件及大撕裂分支的发散模。
AI 中文摘要
我们研究了二次模型$F(R,\mathcal G)=R+\alpha R^2+\beta\mathcal G^2$中的均匀宇宙学扰动。修正的Friedmann方程与尘埃守恒一起线性化，得到均匀Hubble扰动的二阶方程，或等价地，物质对比度的三阶方程。然后我们将渐近分析限制在满足同一二次理论零阶方程的背景上。除了趋近$H=2/(3t)$的低曲率尘埃分支外，该模型还允许一个非平凡的真空de Sitter解，其中$\beta H_{\rm dS}^6=1/96$。其均匀曲率模仅在$\alpha<-1/(6H_{\rm dS}^2)$时稳定。在高曲率下，背景方程还允许一个以$H=7/(t_s-t)$开始的真空大撕裂渐近分支；首阶修正由二次耦合固定。相应的$\mathcal G^2$主导扰动具有一个发散的均匀模。同时的Einstein极限仅作为一致性检验，并恢复标准尘埃行为。
英文摘要
5We study homogeneous cosmological perturbations in the quadratic model $F(R,\mathcal G)=R+αR^2+β\mathcal G^2$. Linearization of the modified Friedmann equation together with dust conservation yields a second-order equation for the homogeneous Hubble perturbation, or equivalently a third-order equation for the matter contrast. We then restrict the asymptotic analysis to backgrounds that satisfy the zeroth-order equations of the same quadratic theory. Besides the low-curvature dust branch, which approaches $H=2/(3t)$, the model admits a nontrivial vacuum de Sitter solution with $βH_{\rm dS}^6=1/96$. Its homogeneous curvature modes are stable only when $α<-1/(6H_{\rm dS}^2)$. At high curvature the background equation also admits a vacuum big-rip asymptotic branch beginning with $H=7/(t_s-t)$; the first corrections are fixed by the quadratic couplings. The corresponding $\mathcal G^2$-dominated perturbation has one divergent homogeneous mode. The simultaneous Einstein limit is taken only as a consistency check and recovers the standard dust behavior.
Comments5 pages
