Reconstructing the distortion function for nonlocal cosmology

We consider the cosmology of modified gravity models in which Newton's constant is distorted by a function of the inverse d'Alembertian acting on the Ricci scalar. We derive a technique for choosing the distortion function so as to fit an arbitrary expansion history. This technique is applied numerically to the case of Lambda CDM cosmology, and the result agrees well with a simple hyperbolic tangent.