标题： 多元宇宙与通过共芬斯勒空间的宇宙繁衍 — 或 — 存在与虚无 显示英文标题

标题： The Multiverse and Cosmic Procreation via Cofinsler Spaces -- or -- Being and Nothingness

摘要： 在本文中，我将考虑一种标量-标量场理论，在四维流形 M 上有一个标量场 phi，并且在 T*M 上有一个洛伦兹共芬斯勒函数 f。选择了一个特别简单的拉格朗日量来支配这种理论，当 f 被选为在 M 上生成 FLRW 度规时，拉格朗日量成为 phi 及其前两个时间导数的函数。相关的哈密顿量是三阶的，并且具有无限多个真空解。这些真空解可以拼接起来生成一个多元宇宙。这是针对那些 k>0 的 FLRW 空间进行的。因此，当时间 t 小于零时，我们有一个宇宙，在其中 t=常数的空间是具有常曲率 k 的 3 球面。随着时间经过零点，底层的四维空间分裂成无限多个空间（分支），其度规张量描述分段的德西特空间，直到某个截止时间，这个截止时间通常对于不同的分支是不同的。在通过截止时间之后，所有分支都会回到它们原来的四维空间，在其中 t=常数的空间具有常曲率 k，但会与其他所有分支宇宙保持分离。这个多元宇宙的度规张量在所有地方都是连续的，但在宇宙分支在不同德西特空间之间变化时会出现不连续的导数。我使用这种形式主义来解决一些问题：当 t<0 时物质的性质是什么；当时间经过 t=0 时物质会发生什么；以及在多个宇宙在 t=0 时出现之前宇宙在做什么。这些问题的答案将有助于解释本文的标题。我还将简要讨论一种可能的量子化空间的方法，膨胀如何影响构成空间的基本单元，以及引力子可能如何起作用。 显示英文摘要

摘要： In this paper I shall consider a scalar-scalar field theory with scalar field phi on a four-dimensional manifold M, and a Lorentzian Cofinsler function f on T*M. A particularly simple Lagrangian is chosen to govern this theory, and when f is chosen to generate FLRW metrics on M the Lagrangian becomes a function of phi and its first two time derivatives. The associated Hamiltonian is third-order, and admits infinitely many vacuum solutions. These vacuum solutions can be pieced together to generate a multiverse. This is done for those FLRW spaces with k>0. So when time, t, is less than zero we have a universe in which the t=constant spaces are 3-spheres with constant curvature k. As time passes through zero the underlying 4-space splits into an infinity of spaces (branches) with metric tensors that describe piecewise de Sitter spaces until some cutoff time, which will, in general, be different for different branches. After passing through the cutoff time all branches will return to their original 4-space in which the t=constant spaces are of constant curvature k, but will remain separate from all of the other branch universes. The metric tensor for this multiverse is everywhere continuous, but experiences discontinuous derivatives as the universe branches change between different de Sitter spaces. Some questions I address using this formalism are: what is the nature of matter when t<0; what happens to matter as time passes through t=0; and what was the universe doing before the multiple universes came into existence at t=0? The answers to these questions will help to explain the paper's title. I shall also briefly discuss a possible means of quantizing space, how inflation influences the basic cells that constitute space, and how gravitons might act.