Phenomenological and Theoretical Aspects of Quantum Gravity

量子力学和广义相对论是两个最成功的物理理论。然而，它们似乎互不相容。量子引力（QG）的候选理论，如超弦理论（ST）和圈量子引力（LQG）旨在统一两者，并取得了重大进展。然而，没有一个实验或观察支持或反驳任何理论。我的研究的主要重点是寻找QG的实验签名。所有QG理论都预言了一个最小可测长度。我和我的合作者的研究表明，这意味着在所有量子系统中存在普遍的QG效应（Das，Vagenas，PRL 101，221301（2008））。这引起了相当大的乐观情绪，尽管普朗克能量标度，约1016 TeV，随着测量灵敏度的不断提高，QG的签名可以在低能实验室中观察到。 广义相对论最重要的应用之一是宇宙学，它在我们对宇宙大尺度结构的理解方面取得了显著的进展。在这个领域，两个主要的未解决的问题是理解暗物质和暗能量的真实性质，它们共同构成了我们宇宙的95%。我们最近已经证明，超轻玻色子的玻色-爱因斯坦凝聚（BEC）是暗物质和暗能量的可行候选者。BEC的密度解释了暗物质，而它产生的具有负压的量子势解释了暗能量。基于上述动机，并基于我的专业知识，我的研究目标是调查上述领域的三个关键问题。在短期（1-2年）和中期（3-5年），我将：1：在QG中建立最小长度的Lorentz协变描述和相关的广义测不准原理（GUP）。应用此方法计算低能系统中的QG校正。在光学机械实验室测量GUP效应。 2：进行定量预测，如宇宙BEC的密度分布，并与现有数据进行比较。 第三章：基于我的团队最近的工作，研究引力希格斯机制作为一个可行的降维模型，并研究其对QG的影响。 我的研究将提供证据支持或反对QG的现有理论，时空的基本维度和暗物质和暗能量的BEC模型。从长远来看，它将为正确的量子引力理论是什么以及如何提取其实验特征提供重要的见解。这将有助于排除一些理论。它还将揭示时空的本质--无论它是基本上离散的还是连续的。它将帮助我们了解宇宙的起源和演变，通过详细的信息，其内容和引力理论，支配它。为了实现这些目标，我将培训HQP在各个层次，并在国内和国际合作。

Quantum Mechanics and General Relativity are two of the most successful physical theories. Yet they appear to be mutually incompatible. Candidate theories of Quantum Gravity (QG) such as Superstring Theory (ST) and Loop Quantum Gravity (LQG) aim to unify the two, and have made significant progress. However, there has not been a single experiment or observation which supports or refutes any theory. The main focus of my research is to find experimental signatures of QG. All QG theories predict a minimum measurable length. The research of my collaborators and I have shown that this implies universal QG effects in all quantum systems (Das, Vagenas, PRL101,221301(2008)). This has given rise to considerable optimism that despite the immensity of the Planck energy scale, about 1016 TeV, with continual improvement in measurement sensitivities, signatures of QG may be observable in the low energy laboratory. One of the most important applications of General Relativity is cosmology, which has made remarkable progress in our understanding of the large scale structure of the universe. Two main unresolved problems in this area are understanding of the true nature of dark matter and dark energy, which together make up 95% of our universe. We have recently shown that a Bose-Einstein condensate (BEC) of ultralight bosons is a viable candidate for both dark matter and dark energy. The density of the BEC accounts for the dark matter and the quantum potential with negative pressure that it generates accounts for the dark energy. Motivated by the above, and building on my expertise, the objective of my research is to investigate three key problems in the aforementioned areas. In the short (1-2 years) and medium term (3-5 years), I will:  1: Formulate a Lorentz covariant description of minimum length and the related Generalized Uncertainty Principle (GUP) in QG. Apply this to compute QG corrections in low energy systems. Measure GUP effects in the optomechanical laboratory.   2: Make quantitative predictions such as density profiles of the cosmic BEC and compare with available data.  3: Building on my team's recent work, study gravitational Higgs mechanism as a viable model of dimensional reduction and study its implications for QG.  My research will provide evidence for or against the existing theories of QG, on the fundamental dimension of spacetime and the BEC model of dark matter and dark energy. In the long term, it will give important insights into what the correct theory of quantum gravity is and how to extract its experimental signatures. It will help rule out some theories. It will also shed light on the nature of spacetime - whether it is fundamentally discrete or continuum. It will help us understand the origin and evolution of the universe via detailed information about its contents and the theory of gravity which governs it.  In order to accomplish these objectives, I will train HQP at all levels and collaborate nationally and internationally.