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Title: Effective description of higher-order scalar-tensor theories

Abstract

Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called 'beyond Horndeski' theories. We also discuss Lorentz-breaking models inspired by Horava gravity.

Authors:
 [1]; ;  [2];  [3]
  1. APC—Astroparticule et Cosmologie, Université Paris Diderot Paris 7, 75013 Paris (France)
  2. Institut de physique théorique, Université Paris Saclay, CEA, CNRS, 91191 Gif-sur-Yvette (France)
  3. Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais, Parc de Grandmont, 37200 Tours (France)
Publication Date:
OSTI Identifier:
22676207
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 05; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; DEGREES OF FREEDOM; DISPERSION RELATIONS; DISPERSIONS; DISTURBANCES; EQUATIONS; GRAVITATION; LAGRANGIAN FUNCTION; MINKOWSKI SPACE; NONLUMINOUS MATTER; PERTURBATION THEORY; SCALAR FIELDS

Citation Formats

Langlois, David, Mancarella, Michele, Vernizzi, Filippo, and Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: michele.mancarella@cea.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: filippo.vernizzi@cea.fr. Effective description of higher-order scalar-tensor theories. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/05/033.
Langlois, David, Mancarella, Michele, Vernizzi, Filippo, & Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: michele.mancarella@cea.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: filippo.vernizzi@cea.fr. Effective description of higher-order scalar-tensor theories. United States. doi:10.1088/1475-7516/2017/05/033.
Langlois, David, Mancarella, Michele, Vernizzi, Filippo, and Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: michele.mancarella@cea.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: filippo.vernizzi@cea.fr. Mon . "Effective description of higher-order scalar-tensor theories". United States. doi:10.1088/1475-7516/2017/05/033.
@article{osti_22676207,
title = {Effective description of higher-order scalar-tensor theories},
author = {Langlois, David and Mancarella, Michele and Vernizzi, Filippo and Noui, Karim, E-mail: langlois@apc.univ-paris7.fr, E-mail: michele.mancarella@cea.fr, E-mail: karim.noui@lmpt.univ-tours.fr, E-mail: filippo.vernizzi@cea.fr},
abstractNote = {Most existing theories of dark energy and/or modified gravity, involving a scalar degree of freedom, can be conveniently described within the framework of the Effective Theory of Dark Energy, based on the unitary gauge where the scalar field is uniform. We extend this effective approach by allowing the Lagrangian in unitary gauge to depend on the time derivative of the lapse function. Although this dependence generically signals the presence of an extra scalar degree of freedom, theories that contain only one propagating scalar degree of freedom, in addition to the usual tensor modes, can be constructed by requiring the initial Lagrangian to be degenerate. Starting from a general quadratic action, we derive the dispersion relations for the linear perturbations around Minkowski and a cosmological background. Our analysis directly applies to the recently introduced Degenerate Higher-Order Scalar-Tensor (DHOST) theories. For these theories, we find that one cannot recover a Poisson-like equation in the static linear regime except for the subclass that includes the Horndeski and so-called 'beyond Horndeski' theories. We also discuss Lorentz-breaking models inspired by Horava gravity.},
doi = {10.1088/1475-7516/2017/05/033},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 05,
volume = 2017,
place = {United States},
year = {Mon May 01 00:00:00 EDT 2017},
month = {Mon May 01 00:00:00 EDT 2017}
}
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