AI 中文总结
研究单场暴胀中萨斯坎德 - 穆哈诺夫方程的动力学对称性，通过叶尔马克夫场映射构建\(sl(2, R)\)生成元和叶尔马克夫 - 刘易斯不变量，应用于德西特空间和慢滚暴胀，得出邦奇 - 戴维斯真空下\(I_{EL} = 1/2\)且非微扰守恒的结论。
AI 中文摘要
我们研究了萨斯坎德 - 穆哈诺夫方程的动力学对称性，该方程支配暴胀期间原初扰动的演化。通过经由满足叶尔马克夫 - 平尼方程的辅助叶尔马克夫场将萨斯坎德 - 穆哈诺夫方程映射到常频率简谐振子，我们构建了相关的\(sl(2, R)\)生成元并导出叶尔马克夫 - 刘易斯不变量。我们将此框架应用于德西特空间和慢滚暴胀，表明邦奇 - 戴维斯真空给出\(I_{EL} = 1/2\)，在慢滚的所有阶次下非微扰守恒。
英文摘要
We investigate the dynamical symmetry of the Sasaki-Mukhanov equation, which governs the evolution of primordial perturbations during inflation. By mapping the Sasaki-Mukhanov equation to a constant-frequency harmonic oscillator via an auxiliary Ermakov field satisfying the Ermakov-Pinney equation, we construct the associated $sl(2, R)$ generators and derive the Ermakov-Lewis invariant. We apply this framework to de Sitter space and slow-roll inflation, demonstrating that the Bunch-Davies vacuum gives $I_{EL} = 1/2$, conserved non-perturbatively at all orders in slow-roll.
Comments13+1 pages; to be published in JKPS
