Higher derivative theories with constraints : Exorcising Ostrogradski's Ghost

By Tai-jun Chen, Matteo Fasiello, Eugene A. Lim, A. Tolley. 2012

163 citations recorded by the source corpus.

We prove that the linear instability in a non-degenerate higher derivative theory, the Ostrogradski instability, can only be removed by the addition of constraints if the original theory's phase space is reduced.

Subfields: Astronomy and Astrophysics, Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/af5e342d813ca23bae34acd1c1f949839a8c3ad7

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Citations in the corpus

Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability (2015, result): “Note that the degeneracy obtained via the coupling to other degrees of freedom naturally provides these constraints in our models, in contrast with the models discussed in [29] where the constraints are imposed by hand.”
On couplings to matter in massive (bi-)gravity (2014, background): “red with respect to at Minkowski metric. The couplings between the two elds ˜and ˇare nothing else but a specic case of a generalised bi-Galileon [97,98] and are thus free of Ostrogadski instability [95,99]. The decoupling limit is thus also free from the BD ghost at the classical level. We now turn”
Healthy degenerate theories with higher derivatives (2016, background): “J C A P 0 7 ( 2 0 1 6 ) 0 3 3 additional constraints in order to reduce the phase space [13].”
Beyond the Cosmological Standard Model (2014, unknown): “(63)For proposals on how to deal with the ghost in this model, see [1010, 1011].”
Cosmological stability bound in massive gravity and bigravity (2013, background): “(7)A field redefinition that includes a finite number of higher time derivatives will always introduce higher time derivatives into the action and hence a ghost by virtue of the Ostrogradski theorem (see [91] for a recent discussion).”