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arXiv 2212.08640gr-qc
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准各向同性宇宙的暴胀量子谱

Inflationary Quantum Spectrum of the Quasi-Isotropic Universe

Nicola Bortolotti, Giovanni Montani

摘要:

我们研究了准各向同性暴胀解的量子动力学。这是通过推导拉格朗日和哈密顿的FLRW背景和非均匀校正,通过扩展的爱因斯坦-希尔伯特行动的二阶扰动振幅。我们这样做的规范不变的时尚采用Mukhanov-Sasaki变量的标量自由度。然后,我们构建的量子动力学的半经典WKB方案的宇宙的非均匀组件被视为一个“小”量子子系统,在经典的各向同性背景上发展。从惠勒-德维特方程出发,我们恢复了微扰的薛定谔动力学,其中由于背景的经典性,出现了波函数的时间依赖性,我们解决了德西特暴胀相位。本文的主要结果是,所得到的标量分量的功率谱具有标准的标度不变的配置文件,而张量的结果是不受通货膨胀的扩展(模的整体归一化因子),因此保留了空间分布的准各向同性校正的度量。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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