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arXiv 1111.7027gr-qcastro-ph.CO
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从群论观点看宇宙学扰动

Cosmological Perturbations from a Group Theoretical Point of View

István Szapudi, Viktor G. Czinner

摘要:

基于李群及其表示理论,提出了一种研究宇宙学扰动的新方法。在从SO(3)考虑重新推导标准协变形式之后,我们给出了一个新的关于Lorentz群不可约表示的扰动Friedmann-Lemaitre-Robertson-Walker(FLRW)度规的展开.结果分解分为(标量,标量),(标量,向量)和(向量,向量)项。这些方程直接对应于标准的Lifshitz分类的宇宙学扰动使用标量,矢量和张量模式,产生于不可约的SO(3)表示的空间部分的度量。虽然洛伦兹群基比SO(3)更好地匹配FLRW时空的局部对称性,但新方程与标准宇宙学扰动理论相比并没有提供进一步的简化。我们猜想这是由于so(3,1)~su(2)x su(2)Lorentz代数不存在与任何平移群生成元交换的交换生成元对.

英文摘要:

We present a new approach to cosmological perturbations based on the theory of Lie groups and their representations. After re-deriving the standard covariant formalism from SO(3) considerations, we provide a new expansion of the perturbed Friedmann-Lemaitre-Robertson-Walker (FLRW) metric in terms of irreducible representations of the Lorentz group. The resulting decomposition splits into (scalar, scalar), (scalar, vector) and (vector, vector) terms. These equations directly correspond to the standard Lifshitz classification of cosmological perturbations using scalar, vector and tensor modes which arise from the irreducible SO(3) representation of the spatial part of the metric. While the Lorentz group basis matches the underlying local symmetries of the FLRW spacetime better than the SO(3), the new equations do not provide further simplification compared to the standard cosmological perturbation theory. We conjecture that this is due to the fact that the so(3,1) ~ su(2) x su(2) Lorentz algebra has no pair of commuting generators commuting with any of the translation group generators.

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