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Title: On the stability conditions for theories of modified gravity in the presence of matter fields

Abstract

We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and a Sorkin-Schutz action for the matter one. Then, we work out the proper viability conditions to guarantee in the scalar sector the absence of ghosts, gradient and tachyonic instabilities. The absence of ghosts can be achieved by demanding a positive kinetic matrix, while the lack of a gradient instability is ensured by imposing a positive speed of propagation for all the scalar modes. In case of tachyonic instability, the mass eigenvalues have been studied and we work out the appropriate expressions. For the latter, an instability occurs only when the negative mass eigenvalue is much larger, in absolute value, than the Hubble parameter. We discuss the results for the minimally coupled quintessence model showing for a particular set of parameters two typical behaviours which in turn lead to a stable and an unstable configuration. Moreover, we find that the speeds of propagation of the scalar modes strongly depend on matter densities, for the beyond Horndeski theories. Our findings can be directlymore » employed when testing modified gravity theories as they allow to identify the correct viability space.« less

Authors:
 [1];  [2];  [3]
  1. Center for Gravitational Physics, Yukawa Institute for Theoretical Physics, Kyoto University, 606-8502, Kyoto (Japan)
  2. Sorbonne Universités, UPMC Univ Paris 6 et CNRS, UMR 7095, Institut d'Astrophysique de Paris, GReCO, 98 bis bd Arago, 75014 Paris (France)
  3. Institute Lorentz, Leiden University, P.O. Box 9506, Leiden 2300 RA (Netherlands)
Publication Date:
OSTI Identifier:
22679979
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 03; 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; 79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; CONFIGURATION; DENSITY; EIGENVALUES; FIELD THEORIES; GRAVITATION; INSTABILITY; NEGATIVE MASS; NONLUMINOUS MATTER; QUANTUM FIELD THEORY; SPACE; STABILITY; TACHYONS; VELOCITY

Citation Formats

De Felice, Antonio, Frusciante, Noemi, and Papadomanolakis, Georgios, E-mail: antonio.defelice@yukawa.kyoto-u.ac.jp, E-mail: fruscian@iap.fr, E-mail: papadomanolakis@lorentz.leidenuniv.nl. On the stability conditions for theories of modified gravity in the presence of matter fields. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/03/027.
De Felice, Antonio, Frusciante, Noemi, & Papadomanolakis, Georgios, E-mail: antonio.defelice@yukawa.kyoto-u.ac.jp, E-mail: fruscian@iap.fr, E-mail: papadomanolakis@lorentz.leidenuniv.nl. On the stability conditions for theories of modified gravity in the presence of matter fields. United States. doi:10.1088/1475-7516/2017/03/027.
De Felice, Antonio, Frusciante, Noemi, and Papadomanolakis, Georgios, E-mail: antonio.defelice@yukawa.kyoto-u.ac.jp, E-mail: fruscian@iap.fr, E-mail: papadomanolakis@lorentz.leidenuniv.nl. Wed . "On the stability conditions for theories of modified gravity in the presence of matter fields". United States. doi:10.1088/1475-7516/2017/03/027.
@article{osti_22679979,
title = {On the stability conditions for theories of modified gravity in the presence of matter fields},
author = {De Felice, Antonio and Frusciante, Noemi and Papadomanolakis, Georgios, E-mail: antonio.defelice@yukawa.kyoto-u.ac.jp, E-mail: fruscian@iap.fr, E-mail: papadomanolakis@lorentz.leidenuniv.nl},
abstractNote = {We present a thorough stability analysis of modified gravity theories in the presence of matter fields. We use the Effective Field Theory framework for Dark Energy and Modified Gravity to retain a general approach for the gravity sector and a Sorkin-Schutz action for the matter one. Then, we work out the proper viability conditions to guarantee in the scalar sector the absence of ghosts, gradient and tachyonic instabilities. The absence of ghosts can be achieved by demanding a positive kinetic matrix, while the lack of a gradient instability is ensured by imposing a positive speed of propagation for all the scalar modes. In case of tachyonic instability, the mass eigenvalues have been studied and we work out the appropriate expressions. For the latter, an instability occurs only when the negative mass eigenvalue is much larger, in absolute value, than the Hubble parameter. We discuss the results for the minimally coupled quintessence model showing for a particular set of parameters two typical behaviours which in turn lead to a stable and an unstable configuration. Moreover, we find that the speeds of propagation of the scalar modes strongly depend on matter densities, for the beyond Horndeski theories. Our findings can be directly employed when testing modified gravity theories as they allow to identify the correct viability space.},
doi = {10.1088/1475-7516/2017/03/027},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 03,
volume = 2017,
place = {United States},
year = {Wed Mar 01 00:00:00 EST 2017},
month = {Wed Mar 01 00:00:00 EST 2017}
}