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Quadratic degenerate higher-order scalar-tensor theories revisited

Abstract : We present a novel and remarkably simple formulation of degenerate higher-order scalar-tensor (DHOST) theories whose Lagrangian is quadratic in the second derivatives of some scalar field. Using disformal transformations of the metric, we identify a special “frame” (or metric) for which the Lagrangian of quadratic DHOST theories reduces to the usual Einstein-Hilbert term plus a few terms that depend on simple geometric quantities characterizing the uniform scalar-field hypersurfaces. In particular, for quadratic DHOST theories in the physically interesting class Ia, the Lagrangian simply consists of the Einstein-Hilbert term plus a term proportional to the three-dimensional scalar curvature of the uniform scalar-field hypersurfaces. The classification of all quadratic DHOST theories becomes particularly transparent in this geometric reformulation, which also applies to scalar-tensor theories that are degenerate only in the unitary gauge.
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https://hal.archives-ouvertes.fr/hal-03098882
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Submitted on : Tuesday, January 5, 2021 - 10:05:33 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:35 PM

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David Langlois, Karim Noui, Hugo Roussille. Quadratic degenerate higher-order scalar-tensor theories revisited. Physical Review D, American Physical Society, 2021, 103 (8), pp.084022. ⟨10.1103/PhysRevD.103.084022⟩. ⟨hal-03098882⟩

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