Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order

2016/08/31 by Jibril Ben Achour, Marco Crisostomi, Kazuya Koyama +4 · 9 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Conformal map #Cosmology and Gravitation Theories #Degenerate energy levels #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Order (exchange) #Physics #Pulsars and Gravitational Waves Research #Pure mathematics #Quadratic equation #Quantum mechanics #Scalar (mathematics) #Scalar field #Tensor (intrinsic definition) #Theoretical physics #astro-ph.CO #gr-qc #hep-th

paper · pdf · doi:10.1007/jhep12(2016)100

published as JHEP 1612 (2016) 100 · 29 pages, published version

openalex publication_date 2016/12/01 · arxiv created 2016/12/22 · arxiv updated 2016/12/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We present all scalar-tensor Lagrangians that are cubic in second derivatives of a scalar field, and that are degenerate, hence avoiding Ostrogradsky instabilities. Thanks to the existence of constraints, they propagate no more than three degrees of freedom, despite having higher order equations of motion. We also determine the viable combinations of previously identified quadratic degenerate Lagrangians and the newly established cubic ones. Finally, we study whether the new theories are connected to known scalar-tensor theories such as Horndeski and beyond Horndeski, through conformal or disformal transformations.

Citations

• Counting the degrees of freedom of generalized Galileons
• The Theorem of Ostrogradsky
• Second-order scalar-tensor field equations in a four-dimensional space
• The galileon as a local modification of gravity
• The Confrontation between General Relativity and Experiment
• Horndeski: beyond, or not beyond?
• Ostrogradsky in theories with multiple fields

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