标题： de Sitter时空中的引力波的量子修正 显示英文标题

标题： Quantum Modifications to Gravity Waves in de Sitter Spacetime

摘要： 我们研究了一个模型，在这个模型中，以空间平坦形式表示的de Sitter时空张量扰动受到无质量共形不变场（例如电磁场）真空涨落效应的修改。 我们使用半经典引力理论，并将共形场应力张量的期望值作为源项。 我们首先通过寻找增长的空间均匀模态来研究de Sitter时空的稳定性，并得出结论：在半经典理论的有效范围内它是稳定的。 接下来，我们考察量子应力张量效应对线性化平面引力波的修正。 我们发现一个校正项，该修正项的形式与原始波相同，但相位偏移了-\pi /2，并且振幅取决于膨胀的持续时间。 此效应的大小与膨胀期间尺度因子的变化成正比。 只要膨胀的能量尺度和初始膨胀时模式的固有频率远低于普朗克尺度，相对校正就很小。 然而，在膨胀开始时处于普朗克尺度以上的模式可能会经历显著的修正。 振幅的增加可能通过修改膨胀宇宙中张量扰动的功率谱而具有可观测的后果。 这种功率谱增强依赖于膨胀的持续时间和波长，短波长时更显著。 显示英文摘要

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 -\pi/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.