On the Emergence of Accelerating Cosmic Expansion in f(R) Theories of
  Gravity
  We consider cosmological modelling in $f(R)$ theories of gravity, using both
top-down and bottom-up constructions. The top-down models are based on
Robertson-Walker geometries, and the bottom-up constructions are built by
patching together sub-horizon-sized regions of perturbed Minkowski space. Our
results suggest that these theories do not provide a theoretically attractive
alternative to the standard general relativistic cosmology. We find that the
only $f(R)$ theories that can admit an observationally viable weak-field limit
have large-scale expansions that are observationally indistinguishable from the
Friedmann solutions of General Relativity with $\Lambda$. Such theories do not
alleviate any of the difficulties associated with $\Lambda$, and cannot produce
any new behaviour in the cosmological expansion without simultaneously
destroying the Newtonian approximation to gravity on small scales.
