Quantum Gravity Effects in Cosmology

这个计划的目标是研究环圈量子引力所预测的早期宇宙中的量子引力效应。 除了建立一个适当的数学框架的困难之外，构建一个成功的量子引力理论的主要障碍是，基本上没有像在量子力学发展中发挥核心作用的实验或观测那样的指导。 这个提议的一个主要目标是通过推导出环量子引力的预测来解决这个问题，这些预测可以通过宇宙微波背景辐射的观测来实际检验，宇宙微波背景辐射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，奇点出现在宇宙学和黑洞时空中，在这一点上，理论崩溃了。 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，这就是在圈量子宇宙学中某些简单时空中所发生的情况，但重要的是要确定在更现实的时空中出现的奇点是否也被量子引力效应解决。 本建议的第二个目的是回答这个问题。 具体来说，我将研究两个关键的开放问题，涉及圈量子引力和它的宇宙学部分。 首先，我将确定如何在全圈量子引力的框架内对一般的宇宙学扰动进行编码，并找到控制它们动力学的方程。 然后，我将使用这些结果来计算圈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进行比较。 其次，我将详细研究一族时空（称为比安奇时空）的量子引力动力学，根据贝林斯基-卡拉特尼科夫-利夫希茨猜想，它可以确定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圈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，并有望推动该领域的进一步重要研究。

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.