Ostrogradsky in theories with multiple fields

de Rham, Claudia; Matas, Andrew

doi:10.1088/1475-7516/2016/06/041

Title: Ostrogradsky in theories with multiple fields

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 upmore » to field redefinitions.« less

Authors:

de Rham, Claudia ^[1]; Matas, Andrew ^[1]

Case Western Reserve Univ., Cleveland, OH (United States). CERCA, Department of Physics

Publication Date:: Thu Jun 23 00:00:00 EDT 2016

Research Org.:: Case Western Reserve Univ., Cleveland, OH (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1434604

Grant/Contract Number:: SC0009946

Resource 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)

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; dark energy theory; modi fied gravity

Citation Formats


                    de Rham, Claudia, and Matas, Andrew. Ostrogradsky in theories with multiple fields.  United States: N. p., 2016. 
Web.  doi:10.1088/1475-7516/2016/06/041.

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                    de Rham, Claudia, & Matas, Andrew. Ostrogradsky in theories with multiple fields.  United States.  https://doi.org/10.1088/1475-7516/2016/06/041

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                    de Rham, Claudia, and Matas, Andrew. Thu .  
"Ostrogradsky in theories with multiple fields".  United States.  https://doi.org/10.1088/1475-7516/2016/06/041.  https://www.osti.gov/servlets/purl/1434604.

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@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         = {Thu Jun 23 00:00:00 EDT 2016},

  month        = {Thu Jun 23 00:00:00 EDT 2016}

}

Copy to clipboard

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Alive and well: mimetic gravity and a higher-order extension in light of GW170817
text, January 2018

Casalino, Alessandro; Rinaldi, Massimiliano; Sebastiani, Lorenzo
arXiv
DOI: 10.48550/arxiv.1811.06830

On the screening mechanism in DHOST theories evading gravitational wave constraints
text, January 2019

Hirano, Shin'ichi; Kobayashi, Tsutomu; Yamauchi, Daisuke
arXiv
DOI: 10.48550/arxiv.1903.08399

2-form gauge theory dual to scalar-tensor theory
text, January 2019

Yoshida, Daisuke
arXiv
DOI: 10.48550/arxiv.1906.02462

Perturbations of Stealth Black Holes in DHOST Theories
text, January 2019

de Rham, Claudia; Zhang, Jun
arXiv
DOI: 10.48550/arxiv.1907.00699

New class of Proca interactions
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de Rham, Claudia; Pozsgay, Victor
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DOI: 10.48550/arxiv.2003.13773

Ghost condensation and Ostrogradskian instability on low derivative backgrounds
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Lopez-Sarrion, Justo; Valencia-Villegas, Mauricio
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DOI: 10.48550/arxiv.2011.04008

Quadratic DHOST theories revisited
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Langlois, David; Noui, Karim; Roussille, Hugo
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DOI: 10.48550/arxiv.2012.10218

Perturbations and quasi-normal modes of black holes with time-dependent scalar hair in shift-symmetric scalar-tensor theories
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Tomikawa, Keitaro; Kobayashi, Tsutomu
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DOI: 10.48550/arxiv.2101.03790

New effective theories of gravitation and their phenomenological consequences
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Torralba, Francisco José Maldonado
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DOI: 10.48550/arxiv.2101.11523

Cosmic structures in Ricci-inverse theories of gravity
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Scomparin, Mattia
arXiv
DOI: 10.48550/arxiv.2102.04676

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Ostrogradsky in theories with multiple fields

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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 dynamicalmore »« less
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We have recently proposed a new class of gravitational scalar-tensor theories free from Ostrogradski instabilities, in ref. [1]. As they generalize Horndeski theories, or ''generalized'' galileons, we call them G{sup 3}. These theories possess a simple formulation when the time hypersurfaces are chosen to coincide with the uniform scalar field hypersurfaces. We confirm that they contain only three propagating degrees of freedom by presenting the details of the Hamiltonian formulation. We examine the coupling between these theories and matter. Moreover, we investigate how they transform under a disformal redefinition of the metric. Remarkably, these theories are preserved by disformal transformationsmore »« less
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Title: Ostrogradsky in theories with multiple fields

Abstract

Citation Formats

Observation of Gravitational Waves from a Binary Black Hole Merger journal, February 2016

Modified gravity and cosmology journal, March 2012

Beyond the cosmological standard model journal, March 2015

Cosmological tests of modified gravity journal, March 2016

Testing general relativity with present and future astrophysical observations journal, December 2015

Ostrogradsky's theorem on Hamiltonian instability journal, January 2015

Higher derivative theories with constraints: exorcising Ostrogradski's ghost journal, February 2013

Ghost free massive gravity in the Stückelberg language journal, May 2012

Helicity decomposition of ghost-free massive gravity journal, November 2011

Ghosts, strong coupling, and accidental symmetries in massive gravity journal, August 2005

Ghosts in massive gravity journal, September 2005

A formal introduction to Horndeski and Galileon theories and their generalizations journal, October 2013

Inflationary non-Gaussianities in the most general second-order scalar-tensor theories journal, October 2011

Inflation and primordial non-Gaussianities of “generalized Galileons” journal, December 2011

Generalized G-Inflation: --Inflation with the Most General Second-Order Field Equations-- journal, September 2011

New Class of Consistent Scalar-Tensor Theories journal, May 2015

Transforming gravity: From derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian journal, March 2014

Unifying framework for scalar-tensor theories of gravity journal, October 2014

Exploring gravitational theories beyond Horndeski journal, February 2015

Horndeski: beyond, or not beyond? journal, March 2016

Counting the degrees of freedom of generalized Galileons journal, October 2015

Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability journal, February 2016

Extended scalar-tensor theories of gravity journal, April 2016

Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations journal, June 2016

Essential building blocks of dark energy journal, August 2013

A unifying description of dark energy journal, November 2014

Effective theory of dark energy at redshift survey scales journal, February 2016

Effective theory of interacting dark energy journal, August 2015

Generalization of the Fierz-Pauli action journal, August 2010

Resummation of Massive Gravity journal, June 2011

Resolving the Ghost Problem in Nonlinear Massive Gravity journal, January 2012

Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity journal, April 2012

On couplings to matter in massive (bi-)gravity journal, January 2015

Cutoff for extensions of massive gravity and bi-gravity journal, March 2016

New kinetic interactions for massive gravity? journal, August 2014

New kinetic terms for massive gravity and multi-gravity: a no-go in vielbein form journal, October 2015

Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors journal, September 2009

Galileon as a local modification of gravity journal, March 2009

Republication of: The dynamics of general relativity journal, August 2008

Derivative-dependent metric transformation and physical degrees of freedom journal, October 2015

Ghosts and matter couplings in massive gravity, bigravity and multigravity journal, December 2014

Second-order scalar-tensor field equations in a four-dimensional space journal, September 1974

The Λ2 limit of massive gravity journal, April 2016

Can Gravitation Have a Finite Range? journal, December 1972

Vielbein to the rescue? Breaking the symmetric vielbein condition in massive gravity and multigravity journal, July 2015

New Kinetic Terms for Massive Gravity and Multi-gravity: A No-Go in Vielbein Form text, January 2015

Counting the degrees of freedom of generalized Galileons text, January 2015

Derivative-dependent metric transformation and physical degrees of freedom text, January 2015

EFT of interacting spin-2 fields journal, January 2020

A geometrical approach to degenerate scalar-tensor theories journal, February 2017

On the (A)dS decoupling limits of massive gravity journal, September 2018

Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order journal, December 2016

Alive and well: mimetic gravity and a higher-order extension in light of GW170817 journal, December 2018

A new scalar–tensor realization of Hořava–Lifshitz gravity journal, March 2019

Horndeski theory and beyond: a review journal, July 2019

Extended vector-tensor theories journal, January 2017

Effective description of higher-order scalar-tensor theories journal, May 2017

Higher derivative scalar-tensor theory through a non-dynamical scalar field journal, March 2019

Spatially covariant gravity with velocity of the lapse function: the Hamiltonian analysis journal, May 2019

Testing modified gravity at cosmological distances with LISA standard sirens journal, July 2019

Vainshtein regime in scalar-tensor gravity: Constraints on degenerate higher-order scalar-tensor theories journal, July 2019

Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations journal, July 2019

Two-form gauge theory dual to scalar-tensor theory journal, October 2019

Perturbations of stealth black holes in degenerate higher-order scalar-tensor theories journal, December 2019

Cosmological self-tuning and local solutions in generalized Horndeski theories journal, January 2017

Vainshtein mechanism after GW170817 journal, January 2018

Beyond Lovelock gravity: Higher derivative metric theories journal, February 2018

Relativistic stars in degenerate higher-order scalar-tensor theories after GW170817 journal, May 2018

Generalized instantaneous modes in higher-order scalar-tensor theories journal, October 2018

Hamiltonian unboundedness vs stability with an application to Horndeski theory journal, November 2018

Spatially covariant gravity: Perturbative analysis and field transformations journal, May 2019

Dark Energy After GW170817: Dead Ends and the Road Ahead journal, December 2017

Stability of Black Holes and the Speed of Gravitational Waves within Self-Tuning Cosmological Models journal, June 2018

Hořava gravity at a Lifshitz point: A progress report journal, February 2017

Gravity beyond general relativity journal, November 2018

Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review journal, April 2019

Static spherically symmetric solutions in a subclass of Horndeski theories of gravity journal, August 2018

Observation of Gravitational Waves from a Binary Black Hole Merger
journal, February 2016

Modified gravity and cosmology
journal, March 2012

Beyond the cosmological standard model
journal, March 2015

Cosmological tests of modified gravity
journal, March 2016

Testing general relativity with present and future astrophysical observations
journal, December 2015

Ostrogradsky's theorem on Hamiltonian instability
journal, January 2015

Higher derivative theories with constraints: exorcising Ostrogradski's ghost
journal, February 2013

Ghost free massive gravity in the Stückelberg language
journal, May 2012

Helicity decomposition of ghost-free massive gravity
journal, November 2011

Ghosts, strong coupling, and accidental symmetries in massive gravity
journal, August 2005

Ghosts in massive gravity
journal, September 2005

A formal introduction to Horndeski and Galileon theories and their generalizations
journal, October 2013

Inflationary non-Gaussianities in the most general second-order scalar-tensor theories
journal, October 2011

Inflation and primordial non-Gaussianities of “generalized Galileons”
journal, December 2011

Generalized G-Inflation: --Inflation with the Most General Second-Order Field Equations--
journal, September 2011

New Class of Consistent Scalar-Tensor Theories
journal, May 2015

Transforming gravity: From derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
journal, March 2014

Unifying framework for scalar-tensor theories of gravity
journal, October 2014

Exploring gravitational theories beyond Horndeski
journal, February 2015

Horndeski: beyond, or not beyond?
journal, March 2016

Counting the degrees of freedom of generalized Galileons
journal, October 2015

Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
journal, February 2016

Extended scalar-tensor theories of gravity
journal, April 2016

Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations
journal, June 2016

Essential building blocks of dark energy
journal, August 2013

A unifying description of dark energy
journal, November 2014

Effective theory of dark energy at redshift survey scales
journal, February 2016

Effective theory of interacting dark energy
journal, August 2015

Generalization of the Fierz-Pauli action
journal, August 2010

Resummation of Massive Gravity
journal, June 2011

Resolving the Ghost Problem in Nonlinear Massive Gravity
journal, January 2012

Confirmation of the secondary constraint and absence of ghost in massive gravity and bimetric gravity
journal, April 2012

On couplings to matter in massive (bi-)gravity
journal, January 2015

Cutoff for extensions of massive gravity and bi-gravity
journal, March 2016

New kinetic interactions for massive gravity?
journal, August 2014

New kinetic terms for massive gravity and multi-gravity: a no-go in vielbein form
journal, October 2015

Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
journal, September 2009

Galileon as a local modification of gravity
journal, March 2009

Republication of: The dynamics of general relativity
journal, August 2008

Derivative-dependent metric transformation and physical degrees of freedom
journal, October 2015

Ghosts and matter couplings in massive gravity, bigravity and multigravity
journal, December 2014

Second-order scalar-tensor field equations in a four-dimensional space
journal, September 1974

The Λ2 limit of massive gravity
journal, April 2016

Can Gravitation Have a Finite Range?
journal, December 1972

Vielbein to the rescue? Breaking the symmetric vielbein condition in massive gravity and multigravity
journal, July 2015

New Kinetic Terms for Massive Gravity and Multi-gravity: A No-Go in Vielbein Form
text, January 2015

Counting the degrees of freedom of generalized Galileons
text, January 2015

Derivative-dependent metric transformation and physical degrees of freedom
text, January 2015

EFT of interacting spin-2 fields
journal, January 2020

A geometrical approach to degenerate scalar-tensor theories
journal, February 2017

On the (A)dS decoupling limits of massive gravity
journal, September 2018

Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
journal, December 2016

Alive and well: mimetic gravity and a higher-order extension in light of GW170817
journal, December 2018

A new scalar–tensor realization of Hořava–Lifshitz gravity
journal, March 2019

Horndeski theory and beyond: a review
journal, July 2019

Extended vector-tensor theories
journal, January 2017

Effective description of higher-order scalar-tensor theories
journal, May 2017

Higher derivative scalar-tensor theory through a non-dynamical scalar field
journal, March 2019

Spatially covariant gravity with velocity of the lapse function: the Hamiltonian analysis
journal, May 2019

Testing modified gravity at cosmological distances with LISA standard sirens
journal, July 2019

Vainshtein regime in scalar-tensor gravity: Constraints on degenerate higher-order scalar-tensor theories
journal, July 2019

Linear stability analysis of hairy black holes in quadratic degenerate higher-order scalar-tensor theories: Odd-parity perturbations
journal, July 2019

Two-form gauge theory dual to scalar-tensor theory
journal, October 2019

Perturbations of stealth black holes in degenerate higher-order scalar-tensor theories
journal, December 2019

Cosmological self-tuning and local solutions in generalized Horndeski theories
journal, January 2017

Vainshtein mechanism after GW170817
journal, January 2018

Beyond Lovelock gravity: Higher derivative metric theories
journal, February 2018

Relativistic stars in degenerate higher-order scalar-tensor theories after GW170817
journal, May 2018

Generalized instantaneous modes in higher-order scalar-tensor theories
journal, October 2018

Hamiltonian unboundedness vs stability with an application to Horndeski theory
journal, November 2018

Spatially covariant gravity: Perturbative analysis and field transformations
journal, May 2019

Dark Energy After GW170817: Dead Ends and the Road Ahead
journal, December 2017

Stability of Black Holes and the Speed of Gravitational Waves within Self-Tuning Cosmological Models
journal, June 2018

Hořava gravity at a Lifshitz point: A progress report
journal, February 2017

Gravity beyond general relativity
journal, November 2018

Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review
journal, April 2019

Static spherically symmetric solutions in a subclass of Horndeski theories of gravity
journal, August 2018

Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order
text, January 2016

Dark Energy after GW170817: dead ends and the road ahead
text, January 2017

Vainshtein mechanism after GW170817
text, January 2017