The Hidden Scalar Lagrangians within Horndeski Theory

TL;DR

This paper reveals hidden scalar Lagrangians within Horndeski theory, showing they can generate multiple vacuum solutions and predict a multiverse with diverse universe types, including expanding, contracting, and oscillating universes.

Contribution

It introduces a novel method of deriving scalar-tensor theories using two scalar fields that generate the metric, uncovering hidden second-order scalar Lagrangians in Horndeski theory.

Findings

Discovery of hidden second-order scalar Lagrangians in Horndeski theory

Prediction of a multiverse with diverse universe behaviors

Multiple vacuum solutions arising from these hidden Lagrangians

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.