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arXiv 2011.03487gr-qc
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量子宇宙时空中原初场的动力学

Dynamics of primordial fields in quantum cosmological spacetimes

Przemysław Małkiewicz, Artur Miroszewski

摘要:

量子宇宙学模型通常用半经典近似来描述,其中初等几何算子的期望值的平滑演化取代了经典和奇异动力学。这种描述的优点是它们相对简单,并且显示了大宇宙的经典行为。然而,它们可能会平滑一个重要的内部结构,并且需要更详细的处理。本工作的目的是研究基本背景变量的量子不确定性及其对原初引力波的影响。为此,我们建立了一个充满线性正压宇宙流体和引力波的Friedmann-Lemaitre-Robertson-Walker宇宙模型。我们仔细推导了量子时空中微扰的动力学方程。量子化产生了引力辐射的傅里叶模式的运动方程,这是对膨胀宇宙中传播的引力波的通常参量振荡方程的量子扩展。进入增强运动方程的两个来自宇宙学背景的量子效应是:(i)一个排斥势,它解决了大爆炸奇点,并用一个大反弹来代替它;(ii)背景时空动力学变量数值的不确定性。首先,我们研究了前一种效应及其对原始振幅谱的影响,并仔细讨论了反弹尺度与模型物理预言之间的关系。接下来我们研究后一种效应,特别是它可能影响引力波的原始振幅的程度。利用WKB近似,我们找到了振幅谱作为背景时空量子色散函数的解析公式。

英文摘要:

Quantum cosmological models are commonly described by means of semiclassical approximations in which a smooth evolution of the expectation values of elementary geometry operators replaces the classical and singular dynamics. The advantage of such descriptions is that they are relatively simple and display the classical behavior for large universes. However, they may smooth out an important inner structure and to include it a more detailed treatment is needed. The purpose of the present work is to investigate quantum uncertainty in the basic background variables and its influence on primordial gravitational waves. To this end we quantize a model of the Friedmann-Lemaitre-Robertson-Walker universe filled with a linear barotropic cosmological fluid and with gravitational waves. We carefully derive the dynamical equations for the perturbations in quantum spacetime. The quantization yields an equation of motion for the Fourier modes of gravitational radiation, which is a quantum extension to the usual parametric oscillator equation for gravitational waves propagating in an expanding universe. The two quantum effects from the cosmological background that enter the enhanced equation of motion are (i) a repulsive potential resolving the big bang singularity and replacing it with a big bounce and (ii) uncertainties in the numerical values for the background spacetime dynamical variables. First we study the former effect and its consequences for the primordial amplitude spectrum and carefully discuss the relation between the bounce scale and the physical predictions of the model. Next we investigate the latter effect, in particular the extent to which it may affect the primordial amplitude of gravitational waves. Making use of the WKB approximation we find an analytical formula for the amplitude spectrum as a function of the quantum dispersion of the background spacetime.

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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