Universal field equations with covariant solutions

Fairlie, D.B.; Govaerts, Jan; Морозов, А.

doi:10.1016/0550-3213(92)90455-k

Cited by 141 publications

(253 citation statements)

References 7 publications

Supporting

Mentioning

238

Contrasting

Unclassified

Order By: Relevance

“…(6.62) Theories of this type-where the (n + 1)-th order Lagrangian can be built from the equation of motion of the n-th order Lagrangian plus a total derivative-are well studied, and are known as Euler hierarchies [598][599][600][601].…”

Section: Euler Hierarchymentioning

confidence: 99%

Beyond the cosmological standard model

et al. 2015

View full text Add to dashboard Cite

After a decade and a half of research motivated by the accelerating universe, theory and experiment have a reached a certain level of maturity. The development of theoretical models beyond Λ or smooth dark energy, often called modified gravity, has led to broader insights into a path forward, and a host of observational and experimental tests have been developed. In this review we present the current state of the field and describe a framework for anticipating developments in the next decade. We identify the guiding principles for rigorous and consistent modifications of the standard model, and discuss the prospects for empirical tests.We begin by reviewing recent attempts to consistently modify Einstein gravity in the infrared, focusing on the notion that additional degrees of freedom introduced by the modification must "screen" themselves from local tests of gravity. We categorize screening mechanisms into three broad classes: mechanisms which become active in regions of high Newtonian potential, those in which first derivatives of the field become important, and those for which second derivatives of the field are important. Examples of the first class, such as f (R) gravity, employ the familiar chameleon or symmetron mechanisms, whereas examples of the last class are galileon and massive gravity theories, employing the Vainshtein mechanism. In each case, we describe the theories as effective theories and discuss prospects for completion in a more fundamental theory. We describe experimental tests of each class of theories, summarizing laboratory and solar system tests and describing in some detail astrophysical and cosmological tests. Finally, we discuss prospects for future tests which will be sensitive to different signatures of new physics in the gravitational sector.The review is structured so that those parts that are more relevant to theorists vs. observers/experimentalists are clearly indicated, in the hope that this will serve as a useful reference for both audiences, as well as helping those interested in bridging the gap between them.

show abstract

Section: Euler Hierarchymentioning

confidence: 99%

Beyond the cosmological standard model

et al. 2015

View full text Add to dashboard Cite

show abstract

“…Furthermore they also satisfy the recursive relations related to the 'Universal Field Equations', first introduced by Fairlie et. al., [29], and explained more recently within the context of the Galileon [30,27] …”

Section: Probe Brane In De Sitter Slicingmentioning

confidence: 99%

De Sitter Galileon

Burrage

Rham

Heisenberg

2011

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

We generalize the Galileon symmetry and its relativistic extension to a de Sitter background. This is made possible by studying a probe-brane in a flat five-dimensional bulk using a de Sitter slicing. The generalized Lovelock invariants induced on the probe brane enjoy the induced Poincaré symmetry inherited from the bulk, while living on a de Sitter geometry. The nonrelativistic limit of these invariants naturally maintain a generalized Galileon symmetry around de Sitter while being free of ghost-like pathologies. We comment briefly on the cosmology of these models and the extension to the AdS symmetry as well as generic FRW backgrounds.

show abstract

“…Such a class of systems is of interest because reparametrization invariance is a type of gauge invariance which emerges in describing relativistic particles or strings. For some interesting ideas on reparametrization invariant field theories see [9].…”

Section: )mentioning

confidence: 99%

Geometric Hamiltonian formalism for reparameterization-invariant theories with higher derivatives

Dunin-Barkowski

Слепцов

2009

Theor Math Phys

View full text Add to dashboard Cite

Reparametrization invariant Lagrangian theories with higher derivatives are considered. We investigate the geometric structures behind these theories and construct the Hamiltonian formalism in a geometric way. The Legendre transformation which corresponds to the transition from the Lagrangian formalism to the Hamiltonian formalism is non-trivial in this case. The resulting phase bundle, i.e. the image of the Legendre transformation, is a submanifold of some cotangent bundle. We show that in our construction it is always odd-dimensional. Therefore the canonical symplectic two-form from the ambient cotangent bundle generates on the phase bundle a field of the null-directions of its restriction. It is shown that the integral lines of this field project directly to the extremals of the action on the configuration manifold. Therefore this naturally arising field is what is called the Hamilton field. We also express the corresponding Hamilton equations through the generilized Nambu bracket.

show abstract

Universal field equations with covariant solutions

Cited by 141 publications

References 7 publications

Beyond the cosmological standard model

Beyond the cosmological standard model

De Sitter Galileon

Geometric Hamiltonian formalism for reparameterization-invariant theories with higher derivatives

Contact Info

Product

Resources

About