Theoretical and Observational Aspecs in Metric-Affine Gravity: A field theoretic perspective
Adrià Delhom
备注：
PhD thesis. 300 pages (not includding references). A chapter of the thesis missing due to content is awaiting to be published. The file will be updated to include the missing chapter as soon as the content of the chapter is uploaded to arXiv as a preprint
In this PhD thesis we deal with several theoretical and phenomenological apsects of metric-affine theories of gravity. Concretely, we first give a broad introduction to the necessary tools to understand the framework and elaborate on some subtleties of the minimal coupling prescription between geometry and matter in presence of torsion and nonmetricity. Then we dedicate the central part of the thesis to study the structure of Ricci Based gravity (RBG) theories, which will be of later use to understand generic properties of metric-affine theories. We begin by analysing the structure of the RBG field equations and nontrivial aspects of their solution space. We then analyse the abrosption spectra of some spherically symmetric solutions. Then, we show that, if the projective symmetry in these theories is explicitly broken, then there arise ghost degrees of freedom, and we argue that this will be a generic feature of metric-affine gravity theories. Having done this, we analyse metricafine theories through the EFT lens, showing how the nonmetricity tkes a particular form in generic theories where the symmetrised Ricci tensor appears in the action beyond the Einstein-Hilbert term. This sources effective interactions that we use to place tight constraints to these theories. In the third part of the thesis we present a miscelanea of works which are not so related to the structure of RBG theories. We begin by studying a model for spontaneous breaking of Lorentz symmetry, namely the bumblebee model, in the metric-affine approach. In the following chapter we generalise a conformal invariant definition of proper time given by Perlick to the case with general nonmetricity. Finally, we present arguments that show that the recently proposed D4EGB theory is not well defined in its original form. We finish with a brief outlook.
本文回顾了Myrzakulov引力模型（MG-N，with $\mathrm{N = I, II, \ldots, VIII}$），导出了它们各自的度量仿射推广（MAMG-N），并讨论了它们的特殊子情形。以度规张量和广义仿射联络为自变量，得到了理论的场方程。然后，我们专注于上述度量仿射模型的功能是线性的情况下，并考虑弗里德曼-Lemaintre-Robertson-Walker背景研究宇宙学方面和应用。
我们给一个简短的大纲，在第二节。2，规范思想应用于内部（$U(1),\, SU(2),\dots$）和外部（$R^4,\,SO(1,3),\dots$）对称性的历史发展，并强调相应守恒流的根本重要性。在第二节中，3.中子干涉仪在地球引力场中的实验结果，用等效原理解释，可以用加速旋转参考系中的狄拉克方程预言。在这样一个非惯性系中使用狄拉克方程，我们描述了如何在规范理论的方法（见表1）中，存在于包含挠率和曲率的黎曼-嘉当时空中的爱因斯坦-嘉当理论作为最简单的引力理论而产生。这与爱因斯坦在黎曼时空中得出广义相对论的方法相反。以秒为单位。\在图4和图5中，我们考虑了物质的守恒能量-动量流，并对相关的平移子群进行了测量。爱因斯坦的远程平行理论的出现被证明是等价的，为无自旋的物质和电磁，广义相对论。在成功地规范了平移之后，就可以直接规范四维仿射群$R^4 \semidirect GL(4,R)$或它的庞加莱子群$R^4\semidirect SO(1,3)$。我们在第二节中简要报告了这些结果。6（metric-affine geometry）and in Sec. 7（度量仿射场方程（\ref{zeroth}，\ref{first}，\ref{second}））。最后，在SEC。8，我们收集了一些模型，目前正在讨论中，它带来了生命的度量仿射规范框架开发。
Reassessing the foundations of Metric-Affine Gravity
Masaryk University（马萨里克大学）；University of Graz（格拉茨大学）；Mons University – UMONS（蒙斯大学）；Politecnico di Torino – PoliTo（都灵理工大学）；Istituto Nazionale di Fisica Nucleare, Section of Torino – INFN（意大利国家核物理研究所都灵分部）
