On the absence of the usual weak-field limit, and the impossibility of
  embedding some known solutions for isolated masses in cosmologies with f(R)
  dark energy
  The problem of matching different regions of spacetime in order to construct
inhomogeneous cosmological models is investigated in the context of Lagrangian
theories of gravity constructed from general analytic functions f(R), and from
non-analytic theories with f(R)=R^n. In all of the cases studied, we find that
it is impossible to satisfy the required junction conditions without the
large-scale behaviour reducing to that expected from Einstein's equations with
a cosmological constant. For theories with analytic f(R) this suggests that the
usual treatment of weak-field systems as perturbations about Minkowski space
may not be compatible with late-time acceleration driven by anything other than
a constant term of the form f(0), which acts like a cosmological constant. In
the absence of Minkowski space as a suitable background for weak-field systems,
one must then choose and justify some other solution to perform perturbative
analyses around. For theories with f(R)=R^n we find that no known spherically
symmetric vacuum solutions can be matched to an expanding FLRW background. This
includes the absence of any Einstein-Straus-like embeddings of the
Schwarzschild exterior solution in FLRW spacetimes.
