  The cosmological phenomenology of gravity is typically studied in two limits:
relativistic perturbation theory (on large scales) and Newtonian gravity
(required for smaller, non-linear, scales). Traditional approaches to
model-independent modified gravity are based on perturbation theory, so do not
apply on non-linear scales. Future surveys such as Euclid will produce
significant data on both linear and non-linear scales, so a new approach is
required to constrain model-independent modified gravity by simultaneously
using all of the data from these surveys. We use the higher order equations
from the post-Friedmann approach to derive a single set of "simple 1PF" (first
post-Friedmann) equations that apply in both the small scale and large scale
limits, and we examine the required conditions for there to be no intermediate
regime, meaning that these simple equations are valid on all scales. We
demonstrate how the simple 1PF equations derived here can be used as a
model-independent framework for modified gravity that applies on all
cosmological scales, and we present an algorithm for determining which modified
gravity theories are subsumed under this approach. This modified gravity
framework provides a rigorous approach to phenomenological N-body simulations,
and paves the way to consistently using all of the data from upcoming surveys
to constrain modified gravity in a model-independent fashion.
