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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-U 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. [ABSTRACT FROM AUTHOR]

Parametrized frameworks for modified gravity are potentially useful tools for model-independent tests of general relativity on cosmological scales. The toy model of an Einstein-de Sitter universe provides a safe test bed in which to improve our understanding of their behavior. We implement a mathematically consistent parametri/ation at the level of the field equations, and use this to calcúlale the evolution of perturbations in an Einstein-de Sitter scenario. Our parametrization explicitly allows for new scalar degrees of freedom, and we compare this to theories in which the only degrees of freedom come from the metric and ordinary matter. The impact on the integrated Sachs-Wolfe effect and canonically conserved superhorizon perturbations is considered. [ABSTRACT FROM AUTHOR]

There is a distinct possibility that current and future cosmological data can be used to constrain Einstein's theory of gravity on the very largest scales. To be able to do this in a model-independent way, it makes sense to work with a general parameterization of modified gravity. Such an approach would be analogous to the Parameterized Post-Newtonian (PPN) approach which is used on the scale of the Solar System. A few such parameterizations have been proposed and preliminary constraints have been obtained. We show that the majority of such parameterizations are only exactly applicable in the quasistatic regime. On larger scales they fail to encapsulate the full behavior of typical models currently under consideration. We suggest that it may be possible to capture the additions to the 'Parameterized Post-Friedmann' (PPF) formalism by treating them akin to fluid perturbations. [ABSTRACT FROM AUTHOR]