大尺度洛伦兹破缺的有效场论

Our former study have already estimated that the dark energy causing the accelerating expansion of the universe originates from the large scale Lorentz violation, some evidences of which are first showed by CMB observation. It can be understood that the large scale Lorentz violation can be regarded as the remnant of the local Lorentz violation during the very early universe era dominating by quantum gravity which is transformed into horizon scale by inflation. Our study also estimates that the common feather of large scale effective gravity with Lorentz violation is that the gravitational source matter distribution can induce the accompanying non-trivial contortion distribution as its dark partner. We will employ the conformal gravity as the high energy gravitational model. The confinement or condensation of Lorentz connection onto Levi-Civita one will ensure the consistency of low energy effective theory with general relativity. The partly confined phase maybe magnified into horizon scale loosing self interaction and failed transforming into fully confined phase and is transformed into the later large scale Lorentz violation. The mechanism may give prediction to the magnitude of Lorentz violation. The similar approach will also be applied to the large Lorentz violation induced by non-trivial higgs phase in the double Higgs like dynamics of high energy gravity. Employing the very special conformal symmetry, the apparent Lorentz violation can be added into the conformal gravity and its impact on predictions of large scale Lorentz violation will be investigated.

前期研究证实导致宇宙加速膨胀的暗能量源于大尺度洛伦兹破缺，大尺度洛伦兹破缺首先来自于CMB观测，可能源于极早期宇宙量子引力的局域洛伦兹破缺，暴涨将其转变为视界尺度上的洛伦兹破缺。前期工作也证实，洛伦兹破缺的大尺度有效引力其共同特征是伴随物质引力源会产生contortion非平庸分布作为物质引力源分布的“暗伙伴”。用共形引力作为高能引力理论，其低能部分与广义相对论的一致性由联络囚禁或者凝聚到Levi-Civita联络来保证，在暴涨阶段，部分囚禁的相可能会被放大到视界尺度，失去相互作用，未能转变成完全囚禁相，造成后来的大尺度洛伦兹破缺，从而对洛伦兹破缺的程度给出预言。对类双Higgs动力学高能引力模型中非平凡Higgs凝聚相导致的大尺度洛伦兹破缺做类似的研究。借助非常狭义共形对称性，在共形引力中加入显式的洛伦兹破缺，研究其对大尺度洛伦兹破缺预言的影响。

在本项目资助下，基于大尺度洛伦兹破缺的机制，建立了宇宙学挠率与真空能量密度对于宇宙后期加速膨胀起作用的图像，该模型实现了量子引力洛伦兹破缺通过暴涨转化为大尺度洛伦兹破缺的机制；引入有效宇宙学常数的概念，利用非平庸contortion分布替代KKLT真空能量密度提升机制，使得弦景观真空可以直接导致宇宙后期加速膨胀；结合沼泽地猜想第二判据排除了宇宙真空来自沼泽地的可能；对有效宇宙学常数建立了具有Brans-Dicke耦合的quintessence有效场论模型，发现quintessence场的单调下降势与德西特类型势分别对应Brans-Dicke耦合的两个不同相，启示该场论模型可能存在两个固定点；基于共形不变引力模型，求解了contortion非平庸相，给出了普朗克能标处的共形不变性为高能有效引力的普适特征图像，其低能表述与洛伦兹破缺的等价性；结合大尺度洛伦兹破缺模型和非零空间曲率，发现空间曲率非零是宇宙学的一个自洽选项，宇宙空间平坦行的结论需要由观测确定；发现非最小耦合矢量挠率和带表面项的Kerr 度规场对于狄拉克和马约拉纳型费米子的量子散射行为迥异，费米子在非最小耦合的矢量挠率场中散射行为可以提供甄别其费米子类型是马约拉纳还是狄拉克的另类手段；建立了费米子在宇宙挠率场中传播的粒子运动和自旋运动动力学方程，发现费米子在挠率-自旋作用力下绕测地线作进动。求解了带自旋轨道耦合的费米子涡旋解，可将该结果用来讨论史瓦西时空中传播的中微子涡旋波。这些进展和结果对于进一步研究量子引力低能有效理论与洛伦兹破缺有效场论之间的联系，检验大尺度洛伦兹破缺有效场论宇宙学预言都有深远的科学意义。