The Hidden Scalar Lagrangians within Horndeski Theory

Abstract

In this essay I show that there exists a new way to obtain scalar-tensor field theories by combining a special scalar field on the tangent bundle of a four-dimensional manifold with a scalar field on that manifold. 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-Lemaitre-Robertson-Walker type cosmological solutions, that hidden in the Horndeski Lagrangians are non-degenerate 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 a multiverse. The multiverse is comprised of numerous different types of individual universes. E.g., some begin explosively, and then coast along exponentially forever at an accelerated rate, while some begin in that manner, and then stop expanding and contract to their original initial stage.