Hamiltonian analysis of higher derivative scalar-tensor theories

By D. Langlois, K. Noui. 2015

225 citations recorded by the source corpus.

We perform a Hamiltonian analysis of a large class of scalar-tensor Lagrangians which depend quadratically on the second derivatives of a scalar field. By resorting to a convenient choice of dynamical variables, we show that the Hamiltonian can be written in a very simple form, where the Hamiltonian and the momentum constraints are easily identified. In the case of degenerate Lagrangians, which include the Horndeski and beyond Horndeski quartic Lagrangians, our analysis confirms that the dimension of the physical phase space is reduced by the primary and secondary constraints due to the degeneracy, thus leading to the elimination of the dangerous Ostrogradsky ghost. We also present the Hamiltonian formulation for nondegenerate theories and find that they contain four degrees of freedom, including a ghost, as expected. We finally discuss the status of the unitary gauge from the Hamiltonian perspective.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/a7184c0557e3687b50c062a8eb21501d2e4da4a9

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Citations in the corpus

Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order (2016, background): “2 All the details about the complete Hamiltonian analysis of quadratic theories can be found in [20].”
Generalized Proca action for an Abelian vector field (2015, background): “[8–11]), thereby forming the vector Galileon case [12, 13], which was investigated thoroughly [14–21].”
Effective description of higher-order scalar-tensor theories (2017, background): “The full expression for the action in an arbitrary gauge can be found in [27].”
Dark energy and modified gravity in degenerate higher-order scalar–tensor (DHOST) theories: A review (2018, background): “The property that the degeneracy of the Lagrangian implies the absence of any extra scalar degree of freedom has been shown explicity in the general case of quadratic DHOST theories by resorting to a Hamiltonian formulation that uses the variable Q∗ and does not assume any particular gauge [24].”
Horndeski theory and beyond: a review (2019, unknown): “lies the existence of a wider class of healthy scalar-tensor theories than the Horndeski class. Degenerate higher-order scalar-tensor theories have been constructed and investigated systematically in [156, 165, 166, 167, 168, 169]. Let us follow Ref. [156] and consider the extension of Horndeski’s G”
Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations (2016, methodology): “In this section, we summarize the main results obtained in [7], as well as some additional elements derived in [8], and present all the quadratic DHOST theories, i.”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “The construction of this type of beyond Horndeski interactions has created a lot of activities in the literature (see for instance [159, 160, 161, 162]).”
Extended scalar-tensor theories of gravity (2016, methodology): “The most general scalar-tensor theory leading to second order equations of motion, the theory of Horndeski [1, 2], propagates three degrees of freedom (dof) in the vacuum.”