论文标题
准偶然宇宙的通货膨胀量频谱
Inflationary Quantum Spectrum of the Quasi-Isotropic Universe
论文作者
论文摘要
我们研究了准偶然通货膨胀溶液的量子动力学。这是通过在FLRW背景和不均匀校正的情况下得出Lagrangian和Hamiltonian来实现的，这是通过在扰动幅度中的Einstein-Hilbert Action扩展到二阶的。我们以规模不变的方式进行此操作，该方式采用了Mukhanov-Sasaki变量来获得标量自由度。然后，我们根据半经典WKB场景构建量子动力学，宇宙的不均匀成分被视为“小”量子子系统，在经典的各向同性背景上演变。从Wheeler-Dewitt方程式开始，我们恢复了用于扰动的Schrödinger动力学，在该动力扰动中，由于背景的经典性，波浪函数的时间依赖性出现了，并为DE Sitter Efferation阶段解决了它。本文的主要结果是，功率谱的产生标量成分具有标准尺度不变曲线，而张量的结果不受通货膨胀膨胀（Modulo A的总归一化因素）的限制，因此保留了准偶性校正对测量标准的空间分布。
We investigate the quantum dynamics of the quasi-isotropic inflationary solution. This is achieved by deriving the Lagrangian and Hamiltonian for both the FLRW background and the inhomogeneous correction, via an expansion of the Einstein-Hilbert action up to second order in the perturbation amplitudes. We do this in a gauge invariant fashion adopting the Mukhanov-Sasaki variable for the scalar degree of freedom. Then we construct the quantum dynamics in terms of a semiclassical WKB scenario for which the inhomogeneous component of the Universe is treated as a "small" quantum subsystem, evolving on the classical isotropic background. Starting from the Wheeler-DeWitt equation, we recover a Schrödinger dynamics for the perturbations, in which the time dependence of the wave function emerges thanks to the classicality of the background, and we solve it for a de Sitter inflationary phase. The main result of this paper is that the resulting scalar component of the power spectrum has the standard scale invariant profile, while the tensor one results to be not constrained by the inflationary expansion (modulo an overall normalization factor), therefore preserving the spatial distribution of the quasi-isotropic correction to the metric.
