Abstract
We show how to generalize the classical duals found by Gabadadze {\it et al} to a very large class of self-interacting theories. This enables one to adopt a perturbative description beyond the scale at which classical perturbation theory breaks down in the original theory. This is particularly relevant if we want to test modified gravity scenarios that exhibit Vainshtein screening on solar system scales. We recognise the duals as being related to the Legendre transform of the original Lagrangian, and present a practical method for finding the dual in general; our methods can also be applied to self-interacting theories with a hierarchy of strong coupling scales, and with multiple fields. We find the classical dual of the full quintic galileon theory as an example.
Highlights
JHEP07(2012)122 classical background solution on distances Λ−1
We show how to generalize the classical duals found by Gabadadze et al to a very large class of self-interacting theories
This enables one to adopt a perturbative description beyond the scale at which classical perturbation theory breaks down in the original theory
Summary
Let us begin by reviewing one of the examples considered by Gabadadze et al [19], namely, the cubic galileon theory [21], L. where Λ corresponds to the scale at which the interaction term becomes strongly coupled. Where T is the trace of the energy momentum tensor It follows that, classically, the linearised theory around a non-relativistic source of mass M breaks down at the scale,. The linearised theory around a non-relativistic source of mass M breaks down at the scale, To see this we note that the field equations can be schematically written as p2φ −. With ∂μφ conjugate to −bμ and φ conjugate to −λ With this observation, it seems natural to include the canonical kinetic term in the transformation. For a non-relativistic source of mass, M , schematically we have pb(1) + p2b(2)
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