Ostrogradsky in theories with multiple fields

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Title: Ostrogradsky in theories with multiple fields
Authors: De Rham, C
Matas, A
Item 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.
Issue Date: 23-Jun-2016
Date of Acceptance: 16-Jun-2016
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 ( Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Funder's Grant Number: DE-SC0009946
Keywords: Nuclear & Particles Physics
0201 Astronomical And Space Sciences
0202 Atomic, Molecular, Nuclear, Particle And Plasma Physics
Publication Status: Published
Open Access location:;
Article Number: 041
Appears in Collections:Physics
Theoretical Physics

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