Ostrogradsky in theories with multiple fields
File(s)
Published version
Author(s)
de Rham, C
Matas, A
Type
Journal Article
Abstract
We review how the (absence of) Ostrogradsky instability manifests itself in theories with multiple fields. It has recently been appreciated that when multiple fields are present, the existence of higher derivatives may not automatically imply the existence of ghosts. We discuss the connection with gravitational theories like massive gravity and beyond Horndeski which manifest higher derivatives in some formulations and yet are free of Ostrogradsky ghost. We also examine an interesting new class of Extended Scalar-Tensor Theories of gravity which has been recently proposed. We show that for a subclass of these theories, the tensor modes are either not dynamical or are infinitely strongly coupled. Among the remaining theories for which the tensor modes are well-defined one counts one new model that is not field-redefinable to Horndeski via a conformal and disformal transformation but that does require the vacuum to break Lorentz invariance. We discuss the implications for the effective field theory of dark energy and the stability of the theory. In particular we find that if we restrict ourselves to the Extended Scalar-Tensor class of theories for which the tensors are well-behaved and the scalar is free from gradient or ghost instabilities on FLRW then we recover Horndeski up to field redefinitions.
Date Issued
2016-06-23
Date Acceptance
2016-06-16
Citation
Journal of Cosmology and Astroparticle Physics, 2016, 2016 (06)
ISSN
1475-7516
Publisher
IOP Publishing: Hybrid Open Access
Journal / Book Title
Journal of Cosmology and Astroparticle Physics
Volume
2016
Issue
06
Copyright Statement
© The Authors. Article funded by SCOAP3. Content from this work may be used
under the terms of the Creative Commons Attribution 3.0 License (https://creativecommons.org/licenses/by/3.0/).
Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
under the terms of the Creative Commons Attribution 3.0 License (https://creativecommons.org/licenses/by/3.0/).
Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Grant Number
DE-SC0009946
Subjects
Nuclear & Particles Physics
0201 Astronomical And Space Sciences
0202 Atomic, Molecular, Nuclear, Particle And Plasma Physics
Publication Status
Published
Article Number
041