膨胀空间中大尺度量子噪声的抑制机制
Mechanism for the suppression of quantum noise at large scales on expanding space
摘要：
我们提出了一个精确可解的模型，用于在扩展空间中抑制大尺度的量子噪声。在量子理论的德布罗意-玻姆导波公式中，这种抑制是自然产生的，根据这种公式，玻恩概率规则有一个动力学起源。对于辐射主导背景下的标量场，我们构造了随时间演化的波泛函的精确解，并研究了相关场轨迹的性质。它示出的扩展空间上的场模式的时间演化在数学上等价于一个标准谐振子的“延迟时间”，取决于模式的波长。在远超哈伯状态下，等效振子仅在一个哈伯时间内演化，产生一个简单的机制，从而可以在非常大的尺度上抑制玻恩规则的弛豫。我们提出了数值模拟，说明如何膨胀的空间可以导致延迟的松弛在超级哈勃政权。有了这些结果，人们自然会期望在超哈勃波长下抑制量子噪声。这样的抑制可能发生在暴胀前的时代，导致宇宙微波背景的大规模功率不足。
英文摘要：
We present an exactly-solvable model for the suppression of quantum noise at large scales on expanding space. The suppression arises naturally in the de Broglie-Bohm pilot-wave formulation of quantum theory, according to which the Born probability rule has a dynamical origin. For a scalar field on a radiation-dominated background we construct the exact solution for the time-evolving wave functional and study properties of the associated field trajectories. It is shown that the time evolution of a field mode on expanding space is mathematically equivalent to that of a standard harmonic oscillator with a 'retarded time' that depends on the wavelength of the mode. In the far super-Hubble regime the equivalent oscillator evolves over only one Hubble time, yielding a simple mechanism whereby relaxation to the Born rule can be suppressed on very large scales. We present numerical simulations illustrating how the expansion of space can cause a retardation of relaxation in the super-Hubble regime. Given these results it is natural to expect a suppression of quantum noise at super-Hubble wavelengths. Such suppression could have taken place in a pre-inflationary era, resulting in a large-scale power deficit in the cosmic microwave background.
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