发表机构
I.N. Ulyanov Ulyanovsk State Pedagogical University; Bauman Moscow State Technical University（伊尔库茨克国立师范大学; 鲍曼莫斯科国立技术大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文对FRW宇宙中Lovelock引力的动力学做完整定性分析，识别不动点、奇点与演化场景，发现N>4时的“大冲击”场景，并以不同阶数与维数的Lovelock引力实例阐释结论。
AI 中文摘要
我们对充满满足正压物态方程$p=\omega\rho$的理想流体的空间平坦Friedmann-Robertson-Walker（FRW）宇宙中Lovelock引力的宇宙动力学开展完整定性分析。从以黎曼张量独立分量表述的广义N维Friedmann方程出发，我们将动力学约化为哈勃参数$H$的单个自治一阶方程，其右侧为$H^2$的多项式之比，由Lovelock多项式的阶数$n$、时空维数$N$及耦合常数$\alpha_i$确定。这些多项式的实根决定系统的不动点与奇点，二者支配系统的渐近行为。我们对可能的演化场景给出完整分类，识别吸引型与排斥型不动点，定位有效物质密度为负的“幻影区间”，并证明不动点在无限时间达到，而奇点在有限时间达到。对于$N>4$且耦合常数取合适负值时，会出现一种定性全新场景，我们称之为“大冲击（Big Shock）”：宇宙从具有有限密度、有限标度因子，但哈勃参数变化率无穷大的状态起始，取代标准大爆炸。我们以$n=1$、$N=4$（广义相对论），$n=2$、$N=5$（爱因斯坦-高斯-博内引力），以及$n=3$、$N=7$（三次Lovelock引力）为例阐释了该一般性分析。
英文摘要
We perform a complete qualitative analysis of the cosmological dynamics of Lovelock gravity in a spatially flat Friedmann-Robertson-Walker (FRW) universe filled with a perfect fluid obeying a barotropic equation of state $p=ωρ$. Starting from the generalized $N$-dimensional Friedmann equations written in terms of the independent components of the Riemann tensor, we reduce the dynamics to a single autonomous first-order equation for the Hubble parameter $H$, whose right-hand side is a ratio of polynomials in $H^2$ fixed by the order $n$ of the Lovelock polynomial, the number of dimensions $N$, and the coupling constants $α_i$. The real roots of these polynomials determine the fixed points and the singular points of the system, which govern its asymptotic behaviour. We give a complete classification of the possible evolution scenarios, identify the attractive and repulsive fixed points, locate the "phantom intervals" in which the effective matter density becomes negative, and show that fixed points are reached in infinite time whereas singular points are reached in finite time. For $N>4$ and suitable negative couplings a qualitatively new scenario arises, which we call the "Big Shock": the universe starts from a state with finite density and finite scale factor but with an infinite rate of change of the Hubble parameter, replacing the standard Big Bang. The general analysis is illustrated for $n=1$, $N=4$ (general relativity), $n=2$, $N=5$ (Einstein-Gauss-Bonnet gravity), and $n=3$, $N=7$ (cubic Lovelock gravity).
Comments43 pages, 7 figures; v2: second revised version submitted to the European Physical Journal C (added a discussion of the sign-changing equation of state, a remark on spatial curvature and a subsection on energy conditions in the phantom intervals; references added)
