The Parametrized Post-Newtonian-Vainshteinian Formalism
  Light degrees of freedom that modify gravity on cosmological scales must be
"screened" on solar system scales in order to be compatible with data. The
Vainshtein mechanism achieves this through a breakdown of classical
perturbation theory, as large interactions involving new degrees of freedom
become important below the so-called Vainshtein radius. We begin to develop an
extension of the Parameterized Post-Newtonian (PPN) formalism that is able to
handle Vainshteinian corrections. We argue that theories with a unique
Vainshtein scale must be expanded using two small parameters. In this
Parameterized Post-Newtonian-Vainshteinian (PPNV) expansion, the primary
expansion parameter that controls the PPN order is, as usual, the velocity $v$.
The secondary expansion parameter, $\alpha$, controls the strength of the
Vainshteinian correction and is a theory-specific combination of the
Schwarzschild radius and the Vainshtein radius of the source that is
independent of its mass. We present the general framework and apply it to Cubic
Galileon theory both inside and outside the Vainshtein radius. The PPNV
framework can be used to determine the compatibility of such theories with
solar system and other strong-field data.
