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Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

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 property that they are degenerate despite the nondegeneracy of the purely scalar part of their Lagrangian.
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Submitted on : Monday, July 3, 2017 - 5:50:25 PM
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David Langlois, Karim Noui. Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability. JCAP, 2016, 02, pp.034. ⟨10.1088/1475-7516/2016/02/034⟩. ⟨hal-01554319⟩

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