The Parameterized Post-Friedmann Framework for Theories of Modified Gravity: Concepts, Formalism and Examples

TL;DR

The paper introduces the Parameterized Post-Friedmann (PPF) framework, a comprehensive formalism for modeling cosmological perturbations in various modified gravity theories, aiding interpretation of future cosmological data.

Contribution

It develops a unified, versatile parameterization for a wide range of modified gravity models, including those with multiple spin-0 fields, and demonstrates its practical application.

Findings

Constructed the PPF formalism for diverse modified gravity theories.

Provided examples illustrating the application of the PPF framework.

Outlined plans for numerical implementation and observational testing.

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.