发表机构
Imperial College London（帝国理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究分析宇宙热引力模型的均匀解，发现其相空间结构包含三类膨胀轨迹，并推广至冷暗物质非守恒情形，揭示晚期行为的关键分界。
AI 中文摘要
一个涌现引力模型被证明包含相关的涌现洛伦兹不变性破缺和应力-能量守恒的违反。其最简单的平坦尘埃解在晚期加速，且无需真空能量，并已被用作观测检验的解析基准。我们研究该理论的更广泛均匀动力学和解。对于单一非守恒尘埃流体，变量$\Omega_m=\rho/(3H^2)$和$u=(HL_2)^{-1}$构成一个具有精确首次积分的二维自治系统。完整的膨胀解空间分为三类：终止于渐近德西特固定线的轨迹、对应于Isichei和Magueijo解析解的临界轨迹，以及转向并再坍缩的轨迹。然后我们考虑现象学上更清晰的模型，其中仅冷暗物质违反能量守恒（而重子和光子行为正常）。相空间变为三维，具有一条物质排斥线和一个真空固定点线。每个满足$0<u_0<3$的正常吸引真空点具有一个二维稳定片。CDM丰度趋于零的极限是奇异的：有限$u_0$片在包含类宇宙学常数积分常数的轨迹上遇到纯重子平面，而零积分常数重子解保持在$\Omega_b=1$并运行至$u\to\infty$。临界端点$u_0=3$分隔这些晚期行为，并推广了特殊单流体解。
英文摘要
An emergent gravity model was shown to contain an associated emergent breaking of Lorentz invariance and violations of stress-energy conservation. Its simplest flat dust solution accelerates at late times without vacuum energy and has already been used as an analytic benchmark for observational tests. We study the wider homogeneous dynamics and solutions of this theory. For a single non-conserved dust fluid, the variables $Ω_m=ρ/(3H^2)$ and $u=(HL_2)^{-1}$ form a two-dimensional autonomous system with an exact first integral. The complete expanding solution space separates into three classes: trajectories ending on an asymptotically de Sitter fixed line, a critical trajectory corresponding to the analytic solution of Isichei and Magueijo, and trajectories that turn around and recollapse. We then consider the phenomenologically cleaner model in which only cold dark matter violates energy conservation (while the baryons and photons behave as normal). The phase space becomes three-dimensional, with a line of matter repellers and a line of vacuum fixed points. Each normally attracting vacuum point with $0<u_0<3$ possesses a two-dimensional stable sheet. The limit in which the CDM abundance tends to zero is singular: finite-$u_0$ sheets meet the exactly baryonic plane on trajectories containing a cosmological-constant-like integration constant, whereas the zero-integration-constant baryonic solution remains at $Ω_b=1$ and runs to $u\to\infty$. The critical endpoint $u_0=3$ separates these late-time behaviours and generalizes the special single-fluid solution.
