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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 tomodel-independent modified gravity are based on perturbation theory, so do notapply on non-linear scales. Future surveys such as Euclid will producesignificant data on both linear and non-linear scales, so a new approach isrequired to constrain model-independent modified gravity by simultaneouslyusing all of the data from these surveys. We use the higher order equationsfrom the post-Friedmann approach to derive a single set of "simple 1PF" (firstpost-Friedmann) equations that apply in both the small scale and large scalelimits, and we examine the required conditions for there to be no intermediateregime, meaning that these simple equations are valid on all scales. Wedemonstrate how the simple 1PF equations derived here can be used as amodel-independent framework for modified gravity that applies on allcosmological scales, and we present an algorithm for determining which modifiedgravity theories are subsumed under this approach. This modified gravityframework provides a rigorous approach to phenomenological N-body simulations,and paves the way to consistently using all of the data from upcoming surveysto constrain modified gravity in a model-independent fashion.

Cosmological gravity on all scales: simple equations, required conditions, and a framework for modified gravity