Abstract
We study new consistent scalar-tensor theories of gravity recently introduced by Langlois and Noui with potentially interesting cosmological applications. We derive the conditions for the existence of a primary constraint that prevents the propagation of an additional dangerous mode associated with higher order equations of motion. We then classify the most general, consistent scalar-tensor theories that are at most quadratic in the second derivatives of the scalar field. In addition, we investigate the possible connection between these theories and (beyond) Horndeski through conformal and disformal transformations. Finally, we point out that these theories can be associated with new operators in the effective field theory of dark energy, which might open up new possibilities to test dark energy models in future surveys.
Highlights
We show that Extended Scalar-Tensor (EST) theories can be associated with novel Effective Field Theory (EFT) operators for dark energy, which are absent in Horndeski and beyond Horndeski theories
We studied a large class of Extended Scalar-Tensor (EST) theories of gravity recently introduced in [7], which are at most quadratic in second derivatives of the scalar field, and propagate at most three degrees of freedom in the vacuum
We investigated which ones among the new theories admit a healthy Minkowski limit, a necessary condition to apply EST theories to weakly gravitating systems
Summary
The set of Lagrangians Li presented in the Introduction leads to higher order equations of motion. They are generally associated with the Ostrogradsky instabilities, unless there are constraints that forbid the propagation of additional dangerous modes. Primary constraints exist when, passing to the Hamiltonian formalism, all the velocities cannot be expressed in terms of the fields and their conjugate momenta. This translates to relations (constraints) between the fields and momenta that need to be added to the canonical Hamiltonian through Lagrangian multipliers. See e.g. [19,20,21] for works studying the Hamiltonian structure of scalar tensor theories
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