2015/10/31 by David Langlois, Karim Noui · 1 citation
Physics and Astronomy · #astro-ph.CO #gr-qc #hep-th
paper · pdf · doi:10.1088/1475-7516/2016/02/034
published as JCAP 1602 (2016) 02, 034 · 19 pages, no figure
arxiv created 2016/03/04 · arxiv updated 2016/03/07
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.