From k-essence to generalised Galileons

By Cedric Deffayet, Xian Gao, D. Steer, G. Zahariade. 2011

962 citations recorded by the source corpus.

We determine the most general scalar field theories which have an action that depends on derivatives of order two or less, and have equations of motion that stay second order and lower on flat space-time. We show that those theories can all be obtained from linear combinations of Lagrangians made by multiplying a particular form of the Galileon Lagrangian by an arbitrary scalar function of the scalar field and its first derivatives. We also obtain curved space-time extensions of those theories which have second-order field equations for both the metric and the scalar field. This provides the most general extension, under the condition that field equations stay second order, of k-essence, Galileons, k-Mouflage as well as of the kinetically braided scalars. It also gives the most general action for a possible scalar classicalizer with second-order field equations. We discuss the relation between our construction and the Euler hierarchies of Fairlie et al. showing, in particular, that Euler hierarchies allow one to obtain the most general theory when the latter is shift symmetric. As a simple application of our formalism, we give the covariantized version of the conformal Galileon.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/30408473a741c21ea57e2bde9bb6b975548853cf

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Citations in the corpus

Exploring gravitational theories beyond Horndeski (2014, background): “If we insist on having the minimal number of degrees of freedom and equations of motion strictly of second order in derivatives, we end up in the realm of Horndeski—or generalized galileons, G2 theories [10, 9].”
The imperfect fluid behind kinetic gravity braiding (2011, background): “[53]”
Dark energy or modified gravity? An effective field theory approach (2012, background): “These operators are sufficient to describe linear perturbations about FRW cosmologies of very general single field dark energy models, including Horndeski’s theory [26, 27, 28, 29].”
Gravitational wave decay into dark energy (2018, methodology): “ SklodowskaCurie Actions Programme. A Connection with Horndeski and beyond Horndeski theories Following [5], in this appendix we connect the EFT action (1) with the covariant formulation of Horndeski [26,27] and beyond Horndeski [44] theories a la GLPV [23,24]. In particular, let us consider a scala”
Disformal invariance of second order scalar-tensor theories: Framing the Horndeski action (2013, methodology): “As a final result the authors of [19] gave the form of the Lagrangian that preserves the second order equations:”
Degenerate higher order scalar-tensor theories beyond Horndeski and disformal transformations (2016, background): “It has been thought for a long time that the absence of an Ostrogradski ghost demands the Euler-Lagrange equations to be at most second-order, which explains why the literature has been mostly limited to the study of Horndeski’s theories [2, 3] until recently.”
hi_class: Horndeski in the Cosmic Linear Anisotropy Solving System (2016, neutral): “[16].”
Towards a nonsingular bouncing cosmology (2012, background): “The most general form of single scalar field Lagrangian giving rise to second-order field equations in four-dimensional spacetime can be expressed as [51, 52]”
Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability (2015, background): “These models were later rediscovered in constructing general covariant extensions of the galileons that lead to at most second order equations of motion, with the preconception that this requirement was necessary to avoid Ostrogradski ghosts [12, 13].”
Maximal freedom at minimum cost: linear large-scale structure in general modifications of gravity (2014, background): “The Horndeski models are the most general set of theories of a single extra scalar degree of freedom or, equivalently, which have equations of motion with at most second derivatives on any background [43].”