Szekeres瑞士奶酪模型和CMB观测
The Szekeres Swiss Cheese model and the CMB observations
摘要：
本文介绍了Szekeres瑞士奶酪模型在宇宙微波背景（CMB）辐射观测分析中的应用。在大多数情况下，非均匀物质分布对CMB观测的影响是在弗里德曼模型的线性扰动下研究的。然而，由于宇宙结构中的密度对比和外尔曲率很大，这个问题值得用另一种方法来研究。Szekeres模型是爱因斯坦方程的非均匀、非对称和精确解。在这个模型中，光的传播和物质的演化可以精确地计算，而不需要像密度对比度的小振幅这样的近似。这允许以更现实的方式检查光传播效应对所测量的CMB温度波动的贡献。分析结果表明，小尺度非线性不均匀性通过Rees-Sciama效应引起温度在角尺度$θ< 0.24^{\circ}$（$\ell > 750$）上的振幅$10^{-7} - 10^{-5}$的波动。这仍然比在这个角度尺度上测量的温度波动小得多。然而，局部和未补偿的不均匀性可以引起幅度大到$10^{-3}$的温度波动，因此可以负责在角CMB功率谱中观察到的低多极异常。
英文摘要：
This paper presents the application of the Szekeres Swiss Cheese model to the analysis of observations of the cosmic microwave background (CMB) radiation. The impact of inhomogeneous matter distribution on the CMB observations is in most cases studied within the linear perturbations of the Friedmann model. However, since the density contrast and the Weyl curvature within the cosmic structures are large, this issue is worth studying using another approach. The Szekeres model is an inhomogeneous, non-symmetrical and exact solution of the Einstein equations. In this model, light propagation and matter evolution can be exactly calculated, without such approximations as small amplitude of the density contrast. This allows to examine in more realistic manner the contribution of the light propagation effect to the measured CMB temperature fluctuations. The results of such analysis show that small-scale, non-linear inhomogeneities induce, via Rees-Sciama effect, temperature fluctuations of amplitude $10^{-7} - 10^{-5}$ on angular scale $θ< 0.24^{\circ}$ ($\ell > 750$). This is still much smaller than the measured temperature fluctuations on this angular scale.However, local and uncompensated inhomogeneities can induce temperature fluctuations of amplitude as large as $10^{-3}$, and thus can be responsible the low multipoles anomalies observed in the angular CMB power spectrum.
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