Symmetries for Galileons and DBI scalars on curved space

By Garrett Goon, Kurt Hinterbichler, M. Trodden. 2011

161 citations recorded by the source corpus.

We introduce a general class of four-dimensional effective field theories which include curved space Galileons and DBI theories possessing nonlinear shift-like symmetries. These effective theories arise from purely gravitational actions for 3-branes probing higher dimensional spaces. In the simplest case of a Minkowski brane embedded in a higher dimensional Minkowski background, the resulting four-dimensional effective field theory is the Galileon one, with its associated Galilean symmetry and second order equations. However, much more general structures are possible. We construct the general theory and explicitly derive the examples obtained from embedding maximally symmetric branes in maximally symmetric ambient spaces. Among these are Galileons and DBI theories with second order equations that live on de Sitter or anti-de Sitter space, and yet retain the same number of symmetries as their flat space counterparts, symmetries which are highly non-trivial from the 4d point of view. These theories have a rich structure, containing potentials for the scalar fields, with masses protected by the symmetries. These models may prove relevant to the cosmology of both the early and late universe.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/ad4abc6aa0698e3789f7cc3fa68f1ea6ce282014

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Citations in the corpus

Horndeski theory and beyond: a review (2019, background): “By extending the probe brane action, one can similarly derive the generalization of the Galileon whose action is of the particular Horndeski form involving G3, G4, and G5 [38, 39, 40, 41].”
Inflation and String Theory (2014, background): “After gauge fixing, these transformations of φ become global symmetries [715],”
Modified Gravity and Cosmology (2011, background): “This procedure has recently been extended to probe branes that are curved, giving rise to a more general class of effective theories on curved space [545, 544] (see, also [221]).”
A systematic approach to generalisations of General Relativity and their cosmological implications (2018, background): “Clearly, promoting the Galileon interactions to the curved spacetime breaks explicitly the Galileon symmetry, even though generalised Galileon symmetry can be constructed on maximally symmetric backgrounds [53, 54].”
Symmetron Cosmology (2011, background): “This mechanism is central to the phenomenological viability of brane-world modifications of gravity [37]−[52], massive gravity [36], [53]−[61] (see [62] for a review), degravitation models [63]−[66] and galileon theories [67]−[80].”
Zoology of condensed matter: framids, ordinary stuff, extra-ordinary stuff (2015, background): “On the other hand, one can successfully generalize the galileon symmetry to maximally symmetric spacetimes [42, 43], but of course maximal symmetry is gone as soon as gravitational perturbations are taken into account.”