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

By J. B. Achour, M. Crisostomi, K. Koyama, D. Langlois, K. Noui, G. Tasinato. Journal of High Energy Physics, 2016

350 citations recorded by the source corpus.

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.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/8375c6e87633ab8c66b70cfb6e800d6fdeb4ac70

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Citations in the corpus

A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “We can start with the most general Lagrangian up to cubic order in Πμν [160, 164, 162]”
Horndeski theory and beyond: a review (2019, methodology): “ polynomial in φµν. One can do similar manipulation to construct cubic DHOST theories as an extension of Horndeski’s G5 Lagrangian (i.e., DHOST theories whose Lagrangian is a cubic polynomial in φµν) [168], though their classiﬁcation is much more involved. Cubic DHOST theories disformally disconnect”
Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review (2018, methodology): “2 The degeneracy conditions at quadratic order will be given explicitly and the cubic ones can be found in [15].”
Scalar-tensor theories and modified gravity in the wake of GW170817 (2017, methodology): “It was found that, for most classes of DHOST theories classified in [7], the square of the propagation speed of tensor modes and that of the scalar mode have opposite sign, which implies that a gradient instability develops in either the scalar or tensor sector.”
Effective field theory of dark energy: A review (2019, methodology): “[96, 97, 318, 319], the Kinetic Gravity Braiding model [93], the shift symmetric GLPV model [274], the tracking and scaling DHOST theories discussed in Ref.”