Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
- APC, Astroparticule et Cosmologie, CNRS-Université Paris Diderot Paris, 10 rue Alice Domon et Léonie Duquet, Paris Cedex 13, 75205 France (France)
- Laboratoire de Mathématiques et Physique Théorique, Université François Rabelais, Parc de Grandmont, Tours, 37200 France (France)
Theories with higher order time derivatives generically suffer from ghost-like instabilities, known as Ostrogradski instabilities. This fate can be avoided by considering ''degenerate'' Lagrangians, whose kinetic matrix cannot be inverted, thus leading to constraints between canonical variables and a reduced number of physical degrees of freedom. In this work, we derive in a systematic way the degeneracy conditions for scalar-tensor theories that depend quadratically on second order derivatives of a scalar field. We thus obtain a classification of all degenerate theories within this class of scalar-tensor theories. The quartic Horndeski Lagrangian and its extension beyond Horndeski belong to these degenerate cases. We also identify new families of scalar-tensor theories with the property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.
- OSTI ID:
- 22525005
- Journal Information:
- Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 02 Vol. 2016; ISSN 1475-7516
- Country of Publication:
- United States
- Language:
- English
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