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

Abstract

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 Ostrogradski instability, include the quartic Horndenski Lagrangian as well as its quartic extension beyond Horndeski, but also other families of Lagrangians. We study how all these theories transform under general conformal-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 conformal-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 field redefinitions.

arXiv comment22 pages; no figure

References in corpus (25)

• From k-essence to generalised Galileons
• Gravity with a dynamical preferred frame
• Healthy theories beyond Horndeski
• Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
• Transforming gravity: from derivative couplings to matter to second-order scalar-tensor theories beyond the Horndeski Lagrangian
• The Relation between Physical and Gravitational Geometry
• Exploring gravitational theories beyond Horndeski
• Essential Building Blocks of Dark Energy
• Extended Scalar-Tensor Theories of Gravity
• Models of non-relativistic quantum gravity: the good, the bad and the healthy
• Mimetic Dark Matter
• Disformal invariance of second order tensor-scalar theories: framing the Horndeski action
• A unifying description of dark energy
• Inflation in $f(R,\varphi )$-theories and mimetic gravity scenario
• Unifying framework for scalar-tensor theories of gravity
• Horndeski: beyond, or not beyond?
• Disformal Transformations, Veiled General Relativity and Mimetic Gravity
• Derivative-dependent metric transformation and physical degrees of freedom
• Mimetic dark matter, ghost instability and a mimetic tensor-vector-scalar gravity
• The two faces of mimetic Horndeski gravity: disformal transformations and Lagrange multiplier
• Cosmological disformal invariance
• Disformal invariance of curvature perturbation
• Spatially covariant theories of gravity: disformal transformation, cosmological perturbations and the Einstein frame
• Cosmological disformal transformations to the Einstein frame and gravitational couplings with matter perturbations
• Disformally self-tuning gravity

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