瑞士奶酪宇宙中的光锥平均值
Light-cone averages in a swiss-cheese universe
摘要：
我们分析了一个玩具瑞士奶酪宇宙模型来研究平均问题。在我们的模型中，奶酪是EdS模型，洞是从LTB解决方案中构造的。我们研究了光子在瑞士奶酪模型中的传播，找到了一个描述观测量的唯象齐次模型。根据光锥平均值的拟合过程，我们发现膨胀标量不受非均匀性的影响。这是因为球面对称。然而，密度的光锥平均值作为红移的函数受到不均匀性的影响。这种效应的产生是因为，随着宇宙的演化，光子在（大）空隙中的时间越来越多，而不是在（薄）高密度结构中。描述密度光锥平均值的唯象均匀模型与和谐模型相似。虽然瑞士奶酪模型中的唯一来源是物质，但唯象的均质模型表现得好像它有暗能量成分。最后，我们研究了唯象模型的状态方程对非均匀性大小的依赖关系，发现状态方程参数w_0和w_a服从幂律关系，标度指数为1。也就是说，状态方程线性地依赖于光子穿过空隙的距离。我们的结论是，在我们的玩具模型，孔必须有一个目前的大小约为250 Mpc的，能够模仿和谐模型。
英文摘要：
We analyze a toy swiss-cheese cosmological model to study the averaging problem. In our model, the cheese is the EdS model and the holes are constructed from a LTB solution. We study the propagation of photons in the swiss-cheese model, and find a phenomenological homogeneous model to describe observables. Following a fitting procedure based on light-cone averages, we find that the the expansion scalar is unaffected by the inhomogeneities. This is because of spherical symmetry. However, the light-cone average of the density as a function of redshift is affected by inhomogeneities. The effect arises because, as the universe evolves, a photon spends more and more time in the (large) voids than in the (thin) high-density structures. The phenomenological homogeneous model describing the light-cone average of the density is similar to the concordance model. Although the sole source in the swiss-cheese model is matter, the phenomenological homogeneous model behaves as if it has a dark-energy component. Finally, we study how the equation of state of the phenomenological model depends on the size of the inhomogeneities, and find that the equation-of-state parameters w_0 and w_a follow a power-law dependence with a scaling exponent equal to unity. That is, the equation of state depends linearly on the distance the photon travels through voids. We conclude that within our toy model, the holes must have a present size of about 250 Mpc to be able to mimic the concordance model.
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