We study Randall-Sundrum two brane setups with mismatched brane tensions. For the vacuum solutions, boundary conditions demand that the induced metric on each of the branes is either de Sitter, Anti-de Sitter, or Minkowski. For incompatible boundary conditions, the bulk metric is necessarily time-dependent. This introduces a new class of time-dependent solutions with the potential to address cosmological issues and provide alternatives to conventional inflationary (or contracting) scenarios. We take a first step in this paper toward such solutions. One important finding is that the resulting solutions can be very succinctly described in terms of an effective action involving only the induced metric on either one of the branes and the radion field. But the full geometry cannot necessarily be simply described with a single coordinate patch. We concentrate here on the time-dependent solutions but argue that supplemented with a brane stabilization mechanism one can potentially construct interesting cosmological models this way. This is true both with and without a brane stabilization mechanism.

中文翻译：

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具有不匹配膜的几何结构

我们研究了 Randall-Sundrum 两种膜张力不匹配的膜设置。对于真空解，边界条件要求每个膜上的诱导度量是 de Sitter、Anti-de Sitter 或 Minkowski。对于不兼容的边界条件，批量度量必须与时间相关。这引入了一类新的依赖时间的解决方案，有可能解决宇宙学问题，并为传统的通货膨胀（或收缩）情景提供替代方案。我们在本文中向此类解决方案迈出了第一步。一个重要的发现是，最终的解决方案可以非常简洁地描述为仅涉及对膜和无线电场之一的感应度量的有效行动。但是完整的几何结构不一定可以用单个坐标补丁来简单地描述。我们在这里专注于时间相关的解决方案，但认为辅以膜稳定机制，人们可以通过这种方式构建有趣的宇宙学模型。无论有没有膜稳定机制，这都是正确的。