Symmetries for Galileons and DBI scalars on curved space

Abstract

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