Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability - INSPIRE

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Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability

David Langlois
(
- APC, Paris
)
,
Karim Noui
(
- Tours U., CNRS and
- APC, Paris
)

Oct 23, 2015

19 pages

Published in:

JCAP 02 (2016) 034

Published: Feb 12, 2016

e-Print:

1510.06930 [gr-qc]

DOI:

10.1088/1475-7516/2016/02/034

View in:

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Abstract: (IOP)

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.

Note:

19 pages, no figure

derivative: high
scalar tensor
gravitation: higher-order
stability
ghost
time dependence
kinetic

References(32)

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