The most general second-order field equations of bi-scalar-tensor theory in four dimensions

TL;DR

This paper extends Horndeski's scalar-tensor theory to include two scalar fields, identifying all second-order field equations and revealing new terms absent in previous multi-Galileon models.

Contribution

It systematically derives the most general second-order field equations for bi-scalar-tensor theories in four dimensions, expanding the scope of scalar-tensor models.

Findings

Identified all possible second-order terms in bi-scalar-tensor theories.

Discovered new terms not present in generalized multi-Galileons.

Discussed the construction of the corresponding Lagrangian.

Abstract

The Horndeski theory is known as the most general scalar-tensor theory with second-order field equations. In this paper, we explore the bi-scalar extension of the Horndeski theory. Following Horndeski's approach, we determine all the possible terms appearing in the second-order field equations of the bi-scalar-tensor theory. We compare the field equations with those of the generalized multi-Galileons, and confirm that our theory contains new terms that are not included in the latter theory. We also discuss the construction of the Lagrangian leading to our most general field equations.