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The problem of matching different regions of spacetime in order to constructinhomogeneous cosmological models is investigated in the context of Lagrangiantheories of gravity constructed from general analytic functions f(R), and fromnon-analytic theories with f(R)=R^n. In all of the cases studied, we find thatit is impossible to satisfy the required junction conditions without thelarge-scale behaviour reducing to that expected from Einstein's equations witha cosmological constant. For theories with analytic f(R) this suggests that theusual treatment of weak-field systems as perturbations about Minkowski spacemay not be compatible with late-time acceleration driven by anything other thana constant term of the form f(0), which acts like a cosmological constant. Inthe absence of Minkowski space as a suitable background for weak-field systems,one must then choose and justify some other solution to perform perturbativeanalyses around. For theories with f(R)=R^n we find that no known sphericallysymmetric vacuum solutions can be matched to an expanding FLRW background. Thisincludes the absence of any Einstein-Straus-like embeddings of theSchwarzschild exterior solution in FLRW spacetimes.

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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