In this paper, I show that there exists a new way to obtain scalar–tensor field theories by combining a special scalar field on the cotangent bundle with a scalar field on spacetime. These two scalar fields act as a generating function for the metric tensor. When using these two scalar fields in the Horndeski Lagrangians, we discover, while seeking Friedmann–Lemaître–Robertson–Walker-type cosmological solutions, that hidden in the Horndeski Lagrangians are nondegenerate second-order scalar Lagrangians. In accordance with Ostrogradsky’s work, these hidden scalar Lagrangians lead to multiple vacuum solutions, and thereby predict the existence of the multiverse. The multiverse is comprised of numerous different types of individual universes. For example, some begin explosively, and then coast along exponentially forever at an accelerated rate, while others begin in that manner, and then stop expanding and contract.

中文翻译：

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Horndeski 理论中隐藏的标量拉格朗日量

在本文中，我展示了一种通过将余切丛上的特殊标量场与时空上的标量场相结合来获得标量-张量场理论的新方法。这两个标量场充当度量张量的生成函数。当在 Horndeski 拉格朗日算子中使用这两个标量场时，我们发现，在寻找 Friedmann-Lemaître-Robertson-Walker 型宇宙学解的同时，隐藏在 Horndeski 拉格朗日算子中的是非退化的二阶标量拉格朗日算子。根据 Ostrogradsky 的工作，这些隐藏的标量拉格朗日函数导致了多个真空解，从而预测了多元宇宙的存在。多元宇宙由许多不同类型的个体宇宙组成。例如，有些开始爆炸，然后以指数速度永远加速，