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arXiv · 1510.06930

Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

David Langlois·Karim Noui
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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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David Langlois, Karim Noui. 2016-03-04. Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability. https://doi.org/10.1088/1475-7516%2F2016%2F02%2F034

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