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      Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

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          Abstract

          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 intriguing property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.

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          Author and article information

          Journal
          2015-10-23
          2016-03-04
          Article
          10.1088/1475-7516/2016/02/034
          1510.06930
          c79382d4-25af-4d77-9186-c4131d79dca2

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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          Custom metadata
          JCAP 1602 (2016) 02, 034
          19 pages, no figure
          gr-qc astro-ph.CO hep-th

          Cosmology & Extragalactic astrophysics,General relativity & Quantum cosmology,High energy & Particle physics

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