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arXiv 1012.1582gr-qcastro-ph.COhep-th
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de Sitter时空中重力波的量子修正

Quantum Modifications to Gravity Waves in de Sitter Spacetime

Jen-Tsung Hsiang, L. H. Ford, Da-Shin Lee, Hoi-Lai Yu

摘要:

我们处理的模型中的张量扰动的de~Sitter时空,表示为一个空间平坦的模型,被修改的真空涨落的影响,无质量的共形不变场,如电磁场。我们使用半经典引力理论,共形场应力张量的期望值作为源。我们首先通过寻找增长的空间均匀模来研究de~Sitter时空的稳定性,并得出结论,在半经典理论的有效性范围内,它是稳定的。接下来我们考察量子应力张量对线性化平面重力波的影响。我们发现一个修正项,它与原始波具有相同的形式,但相位偏移了-π/2,其振幅取决于暴胀的持续时间。该效应的大小与膨胀期间比例因子的变化成比例。只要暴胀的能量标度和暴胀开始时模的固有频率远低于普朗克标度,分数修正就很小。然而,在暴胀开始时是transplanckian的模式可以经历显著的修正。通过对暴胀宇宙学中张量扰动的功率谱的修改,振幅的增加可能会产生可观察到的后果。这种功率谱的增强取决于膨胀的持续时间,并且对于较短的波长更大。

英文摘要:

We treat a model in which tensor perturbations of de~Sitter spacetime, represented as a spatially flat model, are modified by the effects of the vacuum fluctuations of a massless conformally invariant field, such as the electromagnetic field. We use the semiclassical theory of gravity with the expectation value of the conformal field stress tensor as a source. We first study the stability of de~Sitter spacetime by searching for growing, spatially homogeneous modes, and conclude that it is stable within the limits of validity of the semiclassical theory. We next examine the modification of linearized plane gravity waves by the effects of the quantum stress tensor. We find a correction term which is of the same form as the original wave, but displaced in phase by -π/2, and with an amplitude which depends upon the duration of inflation. The magnitude of this effect is proportional to the change in scale factor during inflation. So long as the energy scale of inflation and the proper frequency of the mode at the beginning of inflation are well below the Planck scale, the fractional correction is small. However, modes which are transplanckian at the onset of inflation can undergo a significant correction. The increase in amplitude can potentially have observable consequences through a modification of the power spectrum of tensor perturbations in inflationary cosmology. This enhancement of the power spectrum depends upon the duration of inflation and is greater for shorter wavelengths.

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