发表机构
Moscow Institute of Physics and Technology; Institute for Information Transmission Problems（莫斯科物理技术学院; 信息传输问题研究所）
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 de Sitter 时空中四次势标量场的孤子解，按常矢量因果性分类，并计算经典作用量，证明 D=4 全局真空跃迁解具有辐射状态方程且放大晚期信号。
AI 中文摘要
我们研究了 de Sitter 时空背景中具有四次势的标量场的经典解。利用 ansatz $\phi=F(X\cdot\xi)$，通过嵌入坐标 $X_\alpha$（环境空间的坐标），我们找到了若干族解析解，这些解根据常矢量 $\xi$ 的因果特性进行分类。对于类时的 $\xi$，解是全局正则的，并描述了围绕极小值的全局振荡或全局真空跃迁；对于类空的 $\xi$，解在全局坐标片中具有奇异性，但在开放切片中是正则的。在 Poincaré 坐标片中，它们对应于收缩的泡泡。我们计算了这些孤子的经典作用量，仅当时空维度 $D \le 5$ 时作用量才是有限的。我们证明了 $D=4$ 的全局真空跃迁解具有辐射状态方程 $w=1/3$。在 $D=4$ 的全局真空跃迁解中，推迟格林函数相对于真空顶部的格林函数获得了增长的尾部，这意味着该跃迁在晚期会放大信号。
英文摘要
We study classical solutions of a scalar field with quartic potential in de Sitter space-time. Using the ansatz $ϕ=F(X\cdotξ)$, via embeding coordinate $X_α$ of the ambiend space we find several families of analytic solutions classified by the causal character of the constant vector $ξ$. For time-like $ξ$, the solutions are globally regular and describe either global oscillations around a minimum or global vacuum transition; for space-like $ξ$, they are singular in the global patch but regular in the open slicing. In the Poincaré patch they correspond to contracting bubbles. We compute the classical actions of these solition which are finite only in spacetime dimensions $D \le 5$. We show that the $D=4$ global vacuum transition solution has the radiation equation of state $w=1/3$. In $D=4$ global vacuum transition solution, the retarded Green's function acquires a growing tail as compared to the Green's function on top of vacuum, implying that the transition amplifies the signal at late times.
Comments14 pages
