Brans-Dicke Galileon and the Variational Principle

This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the Brans-Dicke theory with the cubic self-interaction. This is a modification of the Brans-dicke th...

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Bibliographic Details
Published in:arXiv.org 2016-05
Main Authors: Quiros, Israel, García-Salcedo, Ricardo, Gonzalez, Tame, Horta-Rangel, F Antonio, Saavedra, Joel
Format: Article
Language:English
Subjects:
Derivation
Derivatives
Equations of motion
Graduate studies
Mathematical analysis
Relativity
Tensors
Theory of relativity
Online Access:Get full text
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Summary:This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the Brans-Dicke theory with the cubic self-interaction. This is a modification of the Brans-dicke theory by the addition of a term in the Lagrangian which is non-linear in the derivatives of the scalar field: it contains second-order derivatives. This is the basis of the so-called Brans-Dicke Galileon. We pay special attention to the variational principle and to the algebraic details of the derivation. It is shown how higher order derivatives of the fields appearing in the intermediate computations cancel out leading to second order motion equations. The reader will find useful tips for the derivation of the field equations of modifications of general relativity such as the scalar-tensor theories and \(f(R)\) theories, by means of the (stationary action) variational principle. The content of this paper is specially recommended to those graduate and postgraduate students who are interested in the study of the mentioned modifications of general relativity.
ISSN:2331-8422
DOI:10.48550/arxiv.1605.00326