Classical Duals, Legendre Transforms and the Vainshtein Mechanism

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.

16 pages

References in corpus (7)

• Modified Gravity and Cosmology
• Resummation of Massive Gravity
• Imperfect Dark Energy from Kinetic Gravity Braiding
• General second order scalar-tensor theory, self tuning, and the Fab Four
• Predictive Power of Strong Coupling in Theories with Large Distance Modified Gravity
• Galileon Hairs of Dyson Spheres, Vainshtein's Coiffure and Hirsute Bubbles
• Stealth Acceleration and Modified Gravity

Cited by in corpus (9)

• Finding Horndeski theories with Einstein gravity limits
• Restricted Galileons
• The Parametrized Post-Newtonian-Vainshteinian Formalism
• Galileons and strong gravity
• Parameterised Post-Newtonian Expansion in Screened Regions
• The Parameterized Post-Newtonian-Vainshteinian formalism for the Galileon field
• The effect of screening mechanisms on black hole binary inspiral waveforms
• Two-body problem in theories with kinetic screening
• Vainshtein in the UV and a Wilsonian analysis of derivatively coupled scalars