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 $\mathrm{\Lambda }$. Such theories do not alleviate any of the difficulties associated with $\mathrm{\Lambda }$, and cannot produce any new behaviour in the cosmological expansion without simultaneously destroying the Newtonian approximation to gravity on small scales.