AI 中文总结
本研究在量子宇宙学框架下，分析暴胀子-引力系统波函数纠缠对暴胀能谱的影响，通过两个简化模型推导解析能谱，发现其与标准半经典能谱的偏差显著大于常规量子引力修正。
AI 中文摘要
在量子宇宙学背景下，我们研究了耦合微扰的均匀暴胀子-引力系统的Wheeler--DeWitt方程解中的量子纠缠。描述均匀自由度的波函数与描述微扰的波函数相互纠缠，这可能会对暴胀能谱产生潜在可观测的效应。我们将分析限制在两个具有未来德西特吸引子的简化模型中，同时忽略非绝热效应以及Mukhanov--Sasaki方程中$\u003cmath\u003e\u003cmi mathvariant="script"\u003eO\u003c/mi\u003e\u003cmrow\u003e\u003cmo\u003e(\u003c/mo\u003e\u003cmsup\u003e\u003cmrow class="MJX-TeXAtom-ORD"\u003e\u003cmi\u003eℏ\u003c/mi\u003e\u003c/mrow\u003e\u003cmrow class="MJX-TeXAtom-ORD"\u003e\u003cmi\u003e2\u003c/mi\u003e\u003c/mrow\u003e\u003c/msup\u003e\u003cmo\u003e)\u003c/mo\u003e\u003c/mrow\u003e\u003c/math\u003e$阶的贡献。通过对均匀暴胀子变量求边缘分布，我们得到了所得能谱的解析表达式，且可在有可靠近似的区域内对其进行计算。研究确实产生了与标准半经典能谱的微小偏差，且这些偏差远大于通常在该背景下考虑的量子引力修正。
英文摘要
In the context of quantum cosmology, we study quantum entanglement in solutions of the Wheeler--DeWitt equation for a homogeneous inflaton--gravity system coupled to perturbations. The wave function describing the homogeneous degrees of freedom is entangled with the wave function describing the perturbations, and this may lead to potentially observable effects on the inflationary spectra. We restrict our analysis to two simplified models that admit a future de Sitter attractor, while neglecting non-adiabatic effects and contributions of order $\mathcal{O}(\hbar^2)$ in the Mukhanov--Sasaki equation. Analytical expressions for the resulting spectra are obtained by marginalising over the homogeneous inflaton variable and can be evaluated in regimes where reliable approximations are available. Small deviations from the standard semiclassical spectra are indeed generated, and these are significantly larger than the quantum-gravitational corrections usually considered in this context.
Comments23 pages, 1 figure
