Quantum Gravity Effects in Cosmology

这个提议的目标是研究早期宇宙中的量子引力效应，正如环量子引力所预测的那样。除了开发一个合适的数学框架的困难之外，构建一个成功的量子引力理论的一个主要障碍是，基本上没有来自实验或观察的指导，而这些实验或观察在量子力学的发展中发挥了核心作用。这个提议的一个主要目标是通过推导出环量子引力预测来开始解决这个问题，这个预测可以通过宇宙微波背景的观测来实际验证，宇宙微波背景是大爆炸的微弱余辉，现在已经被测量得非常详细。******此外，在广义相对论中，已知奇点出现在宇宙和黑洞时空中，在这一点上，理论就失效了。人们普遍认为，这表明量子引力效应在这些区域应该很重要，并有望消除奇点。事实上，在环量子宇宙学中，这已经被证明发生在一些简单的时空中，但是确定在更现实的时空中出现的奇点是否也由量子引力效应解决是很重要的。本建议的第二个目标是回答这个问题。******具体来说，我将研究两个关于圈量子引力及其宇宙学领域的关键开放问题。首先，我将决定如何在全圈量子引力的框架内编码一般的宇宙摄动，并找到控制其动力学的方程。然后，我将使用这些结果来计算环量子引力效应如何修改广义相对论的预测，并将这些预测与宇宙微波背景的测量结果进行比较。其次，我将详细研究被称为比安奇时空的一组时空的量子引力动力学，根据Belinski-Khalatnikov-Lifshitz猜想，它可能决定在曲率变得非常大的大范围时空区域中的量子引力效应。******通过提供早期宇宙中环量子引力效应的预测，并在比以前更广泛的时空家族中对潜在奇点分辨率进行定量研究，该项目将为量子引力提供新的见解，并有望刺激该领域进一步的重要研究。

The goal of this proposal is to study quantum gravity effects in the early universe as predicted by loop quantum gravity. Beyond the difficulties related to developing an appropriate mathematical framework, a major obstruction to constructing a successful theory of quantum gravity is that there has been essentially no guidance from experiments or observations like those that played a central role in the development of quantum mechanics. One main objective for this proposal is to start addressing this problem by deriving loop quantum gravity predictions that can realistically be tested by observations of the cosmic microwave background, the faint afterglow of the big bang that has now been measured in incredible detail.******In addition, in general relativity singularities are known to arise in cosmological and black hole space-times, at which point the theory breaks down. It is widely believed that this is an indication that quantum gravity effects should be important in these regions and hopefully remove the singularities. Indeed, this is what has been shown to happen for some simple space-times in loop quantum cosmology, but it is important to determine whether the singularities that arise in more realistic space-times are also resolved by quantum gravity effects. The second objective of this proposal is to answer this question.******To be specific, I will work on two key open problems concerning loop quantum gravity and its cosmological sector. First, I will determine how to encode generic cosmological perturbations within the framework of full loop quantum gravity, and find the equations that govern their dynamics. I will then use these results to compute how loop quantum gravity effects may modify the predictions of general relativity, and compare these predictions to measurements of the cosmic microwave background. Second, I will study in detail the quantum gravity dynamics of a family of space-times, known as Bianchi space-times, that according to the Belinski-Khalatnikov-Lifshitz conjecture may determine quantum gravity effects in a wide range of space-time regions where the curvature becomes very large.******By providing predictions of loop quantum gravity effects in the early universe and giving a quantitative study of potential singularity resolution in a wider family of space-times than before, this project will give new insights into quantum gravity and can be expected to spur further important research in the field.