Generalized instantaneous modes in higher-order scalar-tensor theories

Antonio de Felice (1) , David Langlois (2) , Shinji Mukohyama (3, 1, 4) , Karim Noui (2, 3) , Anzhong Wang (5, 6)

1 CGP - Center for Gravitational Physics [Kyoto]
2 APC (UMR_7164) - AstroParticule et Cosmologie
3 IDP - Institut Denis Poisson
4 Kavli IPMU - Kavli Institute for the Physics and Mathematics of the Universe [Tokyo]
5 Zhejiang University of Technology
6 Baylor University

We consider higher-order, scalar-tensor theories which appear degenerate when restricted to the unitary gauge but are not degenerate in an arbitrary gauge. We dub them U-degenerate theories. We provide a full classification of theories that are either DHOST or U-degenerate and that are quadratic in second derivatives of the scalar field and discuss its extension to cubic and higher-order theories. Working with a simple example of U-degenerate theory, we find that, for configurations in which the scalar field gradient is time-like, the apparent extra mode in such a theory can be understood as a generalized instantaneous, or “shadowy” mode, which does not propagate. Appropriate boundary conditions, required by the elliptic nature of part of the equations of motion, lead to the elimination of the apparent instability associated with this extra mode.

Mots clés: General relativity; alternative theories of gravity; field theory: scalar; higher-order; scalar tensor; boundary condition; field equations; unitary gauge; stability

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Relativité Générale et Cosmologie Quantique [gr-qc]

Antonio de Felice, David Langlois, Shinji Mukohyama, Karim Noui, Anzhong Wang. Generalized instantaneous modes in higher-order scalar-tensor theories. Physical Review D, 2018, 98 (8), pp.084024. ⟨10.1103/PhysRevD.98.084024⟩. ⟨hal-01758129⟩