We show that (1) the Einstein field equations with a perfect fluid source admit a nonlinear superposition of two distinct homogenous Friedman-Lemaitre-Robertson-Walker (FLRW) metrics as a solution, (2) the superposed solution is an inhomogeneous geometry in general, (3) it reduces to a homogeneous one in the two asymptotes which are the early and the late stages of the universe as described by two different FLRW metrics, (4) the solution possesses a scale factor inversion symmetry and (5) the solution implies two kinds of topology changes: one during the time evolution of the superposed universe and the other occurring in the asymptotic region of space.

中文翻译：

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FLRW 宇宙的叠加

我们表明 (1) 具有完美流体源的爱因斯坦场方程允许两个不同的齐次弗里德曼-勒梅特-罗伯逊-沃克 (FLRW) 度量的非线性叠加作为解，(2) 叠加解通常是非齐次几何, (3) 它在两个不同的 FLRW 度量所描述的宇宙的早期和晚期阶段的两个渐近线中简化为同质的，(4) 解具有比例因子反演对称性和 (5) 解意味着两种拓扑变化：一种发生在叠加宇宙的时间演化过程中，另一种发生在空间的渐近区域。