Smooth Cauchy data on S 3 for the Einstein- λ -vacuum field equations with cosmological constant λ > 0 that are sufficiently close to de Sitter data develop into a solution that admits a smooth conformal boundary J + in its future. The conformal Einstein equations determine a smooth conformal extension across J + that defines on ‘the other side’ again a λ -vacuum solution. In this article, we discuss to what extent these properties generalize to the future asymptotic behaviour of solutions to the Einstein- λ equations with matter . We study Friedmann–Lemaitre–Robertson–Walker (FLRW) solutions and the Einstein- λ equations coupled to conformally covariant matter transport equations, to conformally privileged matter equations, and to conformally non-covariant matter equations. We present recent results on the Einstein- λ -perfect-fluid equations with a nonlinear asymptotic dust or asymptotic radiation equation of state. This article is part of a discussion meeting issue ‘At the interface of asymptotics, conformal methods and analysis in general relativity’.

中文翻译：

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具有正 λ 的宇宙论：未来行为的层次结构

平滑柯西数据 S 3 对于爱因斯坦来说—— λ -具有宇宙学常数的真空场方程 λ > 0 与德西特数据足够接近的结果发展成一个允许平滑共形边界的解决方案 J + 在它的未来。这共形爱因斯坦方程确定平滑的保角延伸 J + 再次定义“另一边” λ -真空溶液。在本文中，我们讨论这些属性在多大程度上推广到爱因斯坦方程解的未来渐近行为 λ 与物质的方程。我们研究 Friedmann-Lemaitre-Robertson-Walker (FLRW) 解和 Einstein- λ 与共形协变物质输运方程、共形特权物质方程以及共形非协变物质方程耦合的方程。我们展示了爱因斯坦的最新结果 - λ - 具有非线性的完美流体方程渐近尘埃或者渐近辐射状态方程。本文是讨论会议问题“渐进、共形方法和广义相对论分析的接口”的一部分。