Transforming gravity: From derivative couplings to matter to secondorder scalartensor theories beyond the Horndeski Lagrangian
Abstract
We study the structure of scalartensor theories of gravity based on derivative couplings between the scalar and the matter degrees of freedom introduced through an effective metric. Such interactions are classified by their tensor structure into conformal (scalar), disformal (vector), and extended disformal (traceless tensor), as well as by the derivative order of the scalar field. Relations limited to first derivatives of the field ensure secondorder equations of motion in the Einstein frame and hence the absence of Ostrogradski ghost degrees of freedom. The existence of a mapping to the Jordan frame is not trivial in the general case, and can be addressed using the Jacobian of the frame transformation through its eigenvalues and eigentensors. These objects also appear in the study of different aspects of such theories, including the metric and field redefinition transformation of the path integral in the quantum mechanical description. Although secondorder in the Einstein frame, generic disformally coupled theories are described by higherorder equations of motion in the Jordan frame. This apparent contradiction is solved by the use of a hidden constraint: the contraction of the metric equations with a Jacobian eigentensor provides a constraint relation for the higher field derivatives, which allows one to express the dynamical equations in a secondorder form. This signals a loophole in Horndeski's theorem and allows one to enlarge the set of scalartensor theories which are Ostrogradski stable. The transformed GaussBonnet terms are also discussed for the simplest conformal and disformal relations.
 Publication:

Physical Review D
 Pub Date:
 March 2014
 DOI:
 10.1103/PhysRevD.89.064046
 arXiv:
 arXiv:1308.4685
 Bibcode:
 2014PhRvD..89f4046Z
 Keywords:

 04.50.Kd;
 95.36.+x;
 98.80.k;
 98.80.Cq;
 Modified theories of gravity;
 Dark energy;
 Cosmology;
 Particletheory and fieldtheory models of the early Universe;
 General Relativity and Quantum Cosmology;
 Astrophysics  Cosmology and Nongalactic Astrophysics;
 High Energy Physics  Theory
 EPrint:
 21 pages, 2 figures, 2 tables. Minor changes, version accepted for PRD