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.
Highlights
The Horndeski theory [11] provides a typical working example of the latter approach because it is the most general single scalar-tensor theory with second-order field equations
Multi-field Galileon theory was proposed in the flat spacetime [19,20,21,22]
The covariantization of this multi-field Galileon theory, called generalized multi-Galileon, was considered [23] and conjectured that the theory would correspond to the multi-field extension of the Horndeski theory, that is, the most general multi-field scalar-tensor theory with second order equations of motion
Summary
The first step of the construction of the most general scalar-tensor theory of ref. [11] is to work out the most general equations of motion that are of second order in derivatives and compatible with the general covariance. We generalize this construction to the case with two scalar fields
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