AI 中文总结
研究从宇宙学微扰反作用演化暗能量，通过解析计算与数值模拟结合，利用弗里德曼方程平均形式导出状态方程，发现不同处理方式下暗能量时间依赖性不同，其符号不变，对暗能量行为研究有重要意义。
AI 中文摘要
我们认为，不均匀性的反作用与纯宇宙学常数相结合时，会产生一种状态方程可随时间演化的有效暗能量。我们的解析计算与最近的数值模拟一致，这些模拟表明不均匀性的反作用会在当前时刻左右影响暗能量。其状态方程由弗里德曼方程的平均形式导出，该平均是在固定体积的物质粒子上进行的（不一定是全局的）。当将不均匀性视为均匀背景周围的小扰动时，暗能量获得时间依赖性，至少在扰动的标量模式的二次项中，它会简化为一个边界项。因此，对于全局平均来说它变得可以忽略不计。另一方面，当在梯度展开中微扰地处理不均匀性的空间导数时，暗能量得到相同的时间依赖性，它不再简化为一个边界项。即使对于全局平均或当不均匀性引起的恒定空间曲率可忽略不计时，这种时间依赖性也可能很显著。它在当前时刻左右也保持相同的符号，从而导致暗能量要么始终是幻像，要么永远不是幻像，不允许从一种行为类型转变为另一种行为类型。
英文摘要
We argue that the back-reaction of inhomogeneities, when combined with a pure cosmological constant, produces an effective dark energy whose equation of state can evolve with time. Our analytical computation agrees with recent numerical simulations, which have shown that the back-reaction of inhomogeneities can impact dark energy around the present time. Here, its equation of state is derived from an average version of the Friedmann equations, for which the average is taken over a fixed volume of matter particles (not necessarily global). When treating the inhomogeneities as small perturbations around a homogeneous background, dark energy acquires a time dependence which reduces to a boundary term, at least at quadratic order in the scalar modes of the perturbations. Thus, it becomes negligible for a global average. On the other hand, when treating instead the spatial derivatives of the inhomogeneities perturbatively in a gradient expansion, dark energy gets the same time dependence, which no longer reduces to a boundary term. This time dependence can be significant even for a global average or when the constant spatial curvature induced by the inhomogeneities is negligible. It also keeps the same sign around the present time, thus causing dark energy to remain either always phantom or never phantom, not allowing for any crossing from one type of behaviour to the other.
