The Parameterized Post-Friedmann Framework for Theories of Modified Gravity: Concepts, Formalism and Examples
Tessa Baker, Pedro G. Ferreira, Constantinos Skordis
TL;DR
The paper introduces the Parameterized Post-Friedmann framework (PPF) as a model-independent method to test modified gravity in cosmology by parameterizing linear perturbations with new degrees of freedom beyond GR. It constructs a gauge-invariant, two-derivative formalism that attaches a finite set of time- and scale-dependent coefficients to perturbation variables, linking them to a wide class of theories through a dictionary and constraint relations. The work demonstrates the approach via worked examples (scalar-tensor, Einstein-Aether, DGP, EBI, Hořava-Lifschitz, Horndeski, and a dark fluid) and elaborates on the scale dependence, quasi-static limit, and connections to screening formalisms. The framework is designed for numerical implementation and data-driven discrimination of theories, offering both a powerful tool for interpreting future datasets and a guide for model-building in modified gravity.
Abstract
A unified framework for theories of modified gravity will be an essential tool for interpreting the forthcoming deluge of cosmological data. We present such a formalism, the Parameterized Post-Friedmann framework (PPF), which parameterizes the cosmological perturbation theory of a wide variety of modified gravity models. PPF is able to handle spin-0 degrees of freedom from new scalar, vector and tensor fields, meaning that it is not restricted to simple models based solely on cosmological scalar fields. A direct correspondence is maintained between the parameterization and the underlying space of theories, which allows us to build up a `dictionary' of modified gravity theories and their PPF correspondences. In this paper we describe the construction of the parameterization and demonstrate its use through a number of worked examples relevant to the current literature. We indicate how the formalism will be implemented numerically, so that the dictionary of modified gravity can be pitted against forthcoming observations.