Dark Components and Other Cosmological Mysteries Linked Through Extra Dimensions

对我们宇宙的一个非常有凝聚力的描述已经出现，它以惊人的精确度证实了我们的预期，同时也突出了我们目前理解之外的令人信服的物理学证据。超过95%的宇宙是以暗能量和暗物质的未知形式存在的。暗能量的尺度比暗物质的能量尺度低15个数量级，但它们以相当的比例填充着今天的宇宙。有趣的是，在电弱标度和普朗克标度之间的粒子物理学层次中，暗层次重复出现。试图解决粒子层次的问题已经引起了额外维度的存在，带来了一系列看似无关的宇宙学谜团：维度是如何稳定的？为什么只有三维大？是什么驱动了早期宇宙中的各向异性膨胀？PI提出，宇宙的暗成分通过宇宙的一个简单方面--几何学--与其他看似无关的宇宙学之谜联系在一起。她认为，暗能量是卡西米尔能量，是量子力学在有限空间中的必然结果。卡西米尔能量可以将空间体积向外或向内推，这取决于底层的量子场。场的叠加使力平衡并稳定额外维度。根据文献中现有的建议，暗物质可能与最轻的卡鲁扎-克莱因粒子有关，这是普通量子力学在有限空间中的另一个直接结果。尺度之间的层次结构、维度的稳定性以及早期宇宙各向异性膨胀都可以被理解为这些卡西米尔能量的结果。这个提议的更广泛的影响是，每年都有一到两名来自巴纳德学院（哥伦比亚大学附属女子学院）的本科生参与这项关于暗成分和额外维度的研究。学生将学习解决描述高维宇宙学扩展的简单微分方程系统。她的项目的一个补充方面将涉及通过巴纳德支持的向纽约市高中女生的公共宣传来传播这些想法。

A remarkably cohesive description of our universe has emerged that confirmsexpectations with stunning precision yet simultaneously highlights compelling evidencefor physics beyond our current understanding. Over 95% of the universe is in theunknown form of dark energy and dark matter. The scale of the dark energy is 15 orders of magnitude lower than the energy scale of dark matter, yet they fill the universe in comparable proportions today. The dark hierarchy is repeated, intriguingly, in a particle physics hierarchy between the electroweak scale and the Planck scale. Attempts to address the particle hierarchy have invoked the existence of extra dimensions bringing a seemingly unrelated list of cosmological mysteries: How are the dimensions stabilized? Why are only three dimensions large? What could have driven anisotropic inflation in the early universe?The PI proposes that the dark components of the universe are linked to these otherseemingly unrelated cosmological mysteries through one simple facet of the cosmos itsgeometry. The dark energy, she suggests, is Casimir energy, a necessary consequence ofquantum mechanics on a finite space. Casimir energy can push the volume of space outor in, depending on the underlying quantum fields. A superposition of fields allows oneto balance the forces and stabilize the extra dimensions. The dark matter, followingexisting suggestions in the literature, could be related to a lightest Kaluza-Klein particle,another direct consequence of ordinary quantum mechanics on a finite space. Thehierarchy between scales, stabilization of dimensions, as well as early universeanisotropic inflation can be understood as consequences of these Casimir energies.The broader impacts of this proposal are that each year one or two undergraduate students from Barnard College, a women's college affiliated with Columbia University, will be involved in this research on dark components and extra dimensions. The students will learn to solve simple systems of differential equations that describe the expansion of a higher-dimensional cosmology. A complementary aspect of her project will involve dissemination of the ideas through public outreach supported by Barnard to girls in NYC high schools.