Minimal parameterizations for modified gravity
  The increasing precision of cosmological data provides us with an opportunity
to test general relativity (GR) on the largest accessible scales.
Parameterizing modified gravity models facilitates the systematic testing of
the predictions of GR, and gives a framework for detecting possible deviations
from it. Several different parameterizations have already been suggested, some
linked to classifications of theories, and others more empirically motivated.
Here we describe a particular new approach which casts modifications to gravity
through two free functions of time and scale, which are directly linked to the
field equations, but also easy to confront with observational data. We compare
our approach with other existing methods of parameterizing modied gravity,
specifically the parameterized post-Friedmann approach and the older method
using the parameter set $\{\mu,\gamma\}$. We explain the connection between our
parameters and the physics that is most important for generating cosmic
microwave background anisotropies. Some qualitative features of this new
parameterization, and therefore modifications to the gravitational equations of
motion, are illustrated in a toy model, where the two functions are simply
assumed to be constant parameters.
