Modified gravity inside astrophysical bodies
  Many theories of modified gravity, including the well studied Horndeski
models, are characterized by a screening mechanism that ensures that standard
gravity is recovered near astrophysical bodies. In a recently introduced class
of gravitational theories that goes beyond Horndeski, it has been found that
new derivative interactions lead to a partial breaking of the Vainshtein
screening mechanism inside any gravitational source, although not outside. We
study the impact of this new type of deviation from standard gravity on the
density profile of a spherically symmetric matter distribution, in the
nonrelativistic limit. For simplicity, we consider a polytropic equation of
state and derive the modifications to the standard Lane-Emden equations. We
also show the existence of a universal upper bound on the amplitude of this
type of modified gravity, independently of the details of the equation of
state.
