Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations

We consider all degenerate scalar-tensor theories that depend quadratically on second-order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy, in general, ensures the absence of Ostrogradsky's instability, include the quartic Horndeski...

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Bibliographic Details
Published in:Physical review. D 2016-06, Vol.93 (12), Article 124005
Main Authors: Ben Achour, Jibril, Langlois, David, Noui, Karim
Format: Article
Language:English
Subjects:
Astrophysics
Classification
Cosmology
Derivatives
General Relativity and Quantum Cosmology
Gravitation
High Energy Physics - Theory
Instability
Physics
Scalars
Transformations
Transforms
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Summary:We consider all degenerate scalar-tensor theories that depend quadratically on second-order derivatives of a scalar field, which we have identified in a previous work. These theories, whose degeneracy, in general, ensures the absence of Ostrogradsky's instability, include the quartic Horndeski Lagrangian and its quartic extension beyond Horndeski, as well as other Lagrangians. We study how all these theories transform under general disformal transformations and find that they can be separated into three main classes that are stable under these transformations. This leads to a complete classification modulo disformal transformations. Finally, we show that these higher order theories include mimetic gravity and some particular khronometric theories. They also contain theories that do not correspond, to our knowledge, to already studied theories, even up to disformal transformations.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.93.124005