发表机构
Purdue University（普渡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文解析证明sine-Gordon孤子在de Sitter时空中的存在性依赖于质量参数与哈勃常数之比，并启发式推测GUT单极子核心的次级暴胀不可行。
AI 中文摘要
我们解析地证明，在1+1维非动力学de Sitter时空中，若$\alpha:= (m/H)^2 < 2$，其中$m$是sine-Gordon理论的质量参数，$H$是哈勃常数，则静态sine-Gordon孤子不可能存在。相反，我们也证明，当$\alpha > 2$时，静态sine-Gordon孤子在1+1维非动力学de Sitter时空中存在。上述阈值通过一个启发式论证得到了定性的且误差在O(1)因子内的解释，该论证涉及Lorentzian sine-Gordon孤子中的张力与de Sitter时空中的潮汐力之间的相互作用。一个类似的启发式论证（仍有待解析确认）也表明存在一个阈值$(m_V/H)^2 \sim O(1)$，低于该阈值时潮汐力过强，无法允许非动力学3+1维de Sitter时空中存在静态的't Hooft--Polyakov单极子；其中$m_V$是矢量玻色子的质量。Linde曾提出，即使在大统一（GUT）相变时或之后的哈勃常数显著小于$X$玻色子的质量，新暴胀也可能在GUT单极子的核心触发次级暴胀。我们提出一个启发式论证，表明当暴胀背景较弱时，$SO(3)$ 't Hooft--Polyakov单极子不允许在其核心发生次级暴胀。基于上述尚未得到解析确认的关于$SO(3)$ 't Hooft--Polyakov单极子的启发式论证，我们推测GUT单极子核心的次级暴胀是不可行的。
英文摘要
We show, analytically, that a static sine-Gordon soliton cannot exist in 1 + 1 non-dynamical de Sitter spacetime if $α:= (m/H)^2 < 2$, where $m$ is the mass parameter of the sine-Gordon theory and $H$ is the Hubble constant. Conversely, we also show that static sine-Gordon solitons exist in 1 + 1 non-dynamical de Sitter spacetime if $α> 2$. The above threshold is explained---qualitatively and to within an O(1) factor---using a heuristic argument involving the interplay of tensile force in the Lorentzian sine-Gordon soliton and the tidal force in de Sitter spacetime. A similar heuristic argument, which remains to be confirmed analytically, also suggests the existence of a threshold, $ (m_V/H)^2 \sim O(1)$, below which the tidal forces are too strong to permit the existence of a static `t Hooft--Polyakov monopole in non-dynamical 3 + 1 de Sitter spacetime; $m_V$ is the mass of the vector boson. Linde has suggested that new inflation could have triggered secondary inflation at the core of a GUT (Grand Unified Theory) monopole even if the Hubble constant at or after the GUT phase transition was significantly smaller than the mass of the $X$ boson. We present a heuristic argument, which suggests that the $SO(3)$ `t Hooft--Polyakov monopole does not allow secondary inflation at its core when the inflationary background is weak. Based on the above, as yet analytically unconfirmed, heuristic argument for the $SO(3)$ `t Hooft--Polyakov monopole, we conjecture that secondary inflation at the core of a GUT monopole is infeasible.
Comments49 pages, 10 figures
Journal refUniverse 12(4), 119, 2026
