One of the leading ideas for the beginning of the Universe is the Hartle-Hawking ‘No-Boundary Proposal.’ Since the Cobordism Conjecture claims that any spacetime allows for a dynamical boundary, we suggest that one may equally well consider a ‘Boundary Proposal’. Specifically, the corresponding euclidean instanton is a sphere with two holes around north and south pole cut out. Analogously to the Hartle-Hawking proposal, the sphere is then cut in two at the equator and half of it is dropped. The equator is glued to an expanding Lorentzian de Sitter space, implementing a beginning of the Universe with a spacelike spherical boundary at its earliest moment. This process is in principle on equal footing with the one based on the no-boundary instanton. In fact, if the Linde-Vilenkin sign choice is used, this ‘Boundary’ creation process may even dominate. An intriguing implication arises if tensionless end-of-the-world branes, as familiar from type-IIA or M-theory, are available: Analogously to the Boundary Proposal, one may then be able to create a compact, flat torus universe from nothing, without any exponential suppression or enhancement factors.

中文翻译：

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 边界提案


宇宙起源的主要思想之一是哈特尔-霍金的“无边界提议”。由于科博德猜想声称任何时空都允许存在动态边界，因此我们建议人们同样可以考虑“边界提议”。具体来说，相应的欧几里得瞬子是一个在北极和南极周围切出两个孔的球体。与哈特尔-霍金的提议类似，球体在赤道处被切成两半，其中一半被丢弃。赤道粘在一个不断膨胀的洛伦兹德西特空间上，实现了宇宙在最早时刻具有类空间球形边界的开始。这一过程原则上与基于无边界瞬子的过程处于同等地位。事实上，如果使用 Linde-Vilenkin 符号选择，这种“边界”创建过程甚至可能占主导地位。如果无张力的世界末日膜（如 IIA 型或 M 理论中所熟悉的那样）可用，就会出现一个有趣的含义：类似于边界提议，人们可能能够从无到有地创建一个紧凑、平坦的环面宇宙，没有任何指数抑制或增强因子。