各向异性Thurston几何的宇宙学约束
Cosmological constraints on anisotropic Thurston geometries
AI总结：
该研究针对违背宇宙学原理的均匀各向异性Thurston几何时空模型，分析其背景演化引发的CMB温度涨落，结合观测谱得出曲率参数上限，严格约束了这类模型的宇宙学影响。
摘要：
现代宇宙学的诸多研究都建立在宇宙学原理之上，即假设宇宙在足够大的尺度上是各向同性且均匀的，但对轻微违背这一原理的宇宙学模型展开探究仍具有重要价值。我们研究了一类保持均匀性、但因底层局部空间几何而打破各向同性的时空。这类时空具备Thurston几何化定理中的五种各向异性模型几何之一，其演化由理想流体尘埃和宇宙学常数驱动。我们发现，这些时空的背景演化会在观测到的宇宙微波背景（CMB）温度中引发涨落，涨落的幅度与曲率参数$Ω_K$相关。为使这些涨落与观测到的CMB角功率谱相符，我们得出五种几何均要求满足$|Ω_K| \lesssim 10^{-5}$的结论，这一结果强烈限制了这类模型的宇宙学效应。
英文摘要：
Much of modern cosmology relies on the Cosmological Principle, the assumption that the Universe is isotropic and homogeneous on sufficiently large scales, but it remains worthwhile to examine cosmological models that violate this principle slightly. We examine a class of such spacetimes that maintain homogeneity but break isotropy through their underlying local spatial geometries. These spacetimes are endowed with one of five anisotropic model geometries of Thurston's geometrization theorem, and their evolution is sourced with perfect fluid dust and cosmological constant. We show that the background evolution of these spacetimes induces fluctuations in the observed cosmic microwave background (CMB) temperature with amplitudes coupled to the curvature parameter $Ω_K$. In order for these fluctuations to be compatible with the observed CMB angular power spectrum, we find $|Ω_K| \lesssim 10^{-5}$ is required in all five geometries. This strongly limits the cosmological consequences of these models.
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