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Title: Ostrogradsky in theories with multiple fields

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 upmore » to field redefinitions.« less
Authors:
 [1] ;  [1]
  1. Case Western Reserve Univ., Cleveland, OH (United States). CERCA, Department of Physics
Publication Date:
Grant/Contract Number:
SC0009946
Type:
Accepted Manuscript
Journal Name:
Journal of Cosmology and Astroparticle Physics
Additional Journal Information:
Journal Volume: 2016; Journal Issue: 06; Journal ID: ISSN 1475-7516
Publisher:
Institute of Physics (IOP)
Research Org:
Case Western Reserve Univ., Cleveland, OH (United States)
Sponsoring Org:
USDOE
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; dark energy theory; modi fied gravity
OSTI Identifier:
1434604

de Rham, Claudia, and Matas, Andrew. Ostrogradsky in theories with multiple fields. United States: N. p., Web. doi:10.1088/1475-7516/2016/06/041.
de Rham, Claudia, & Matas, Andrew. Ostrogradsky in theories with multiple fields. United States. doi:10.1088/1475-7516/2016/06/041.
de Rham, Claudia, and Matas, Andrew. 2016. "Ostrogradsky in theories with multiple fields". United States. doi:10.1088/1475-7516/2016/06/041. https://www.osti.gov/servlets/purl/1434604.
@article{osti_1434604,
title = {Ostrogradsky in theories with multiple fields},
author = {de Rham, Claudia and Matas, Andrew},
abstractNote = {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.},
doi = {10.1088/1475-7516/2016/06/041},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 06,
volume = 2016,
place = {United States},
year = {2016},
month = {6}
}