We consider radiation from cosmological apparent horizon in Friedmann–Lemaitre–Robertson–Walker (FLRW) model in a double-null coordinate setting. As the spacetime is dynamic, there is no timelike Killing vector, instead we have Kodama vector which acts as dynamical time. We construct the positive frequency modes of the Kodama vector across the horizon. The conditional probability that a signal reaches the central observer when it is crossing from the outside gives the temperature associated with the horizon.

中文翻译：

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宇宙视视界温度的估计：一种新方法

我们在双零坐标设置中考虑了弗里德曼-勒梅特-罗伯逊-沃克 (FLRW) 模型中来自宇宙视界的辐射。由于时空是动态的，因此没有像时间一样的杀戮向量，取而代之的是充当动态时间的 Kodama 向量。我们构建了跨越地平线的 Kodama 矢量的正频率模式。信号从外部穿过时到达中心观察者的条件概率给出了与地平线相关的温度。