A Parameterized Post-Friedmann Framework for Modified Gravity

TL;DR

This paper introduces a flexible parameterized framework to describe various regimes of modified gravity models that explain cosmic acceleration without dark energy, facilitating consistency tests of general relativity across different scales.

Contribution

It develops a comprehensive PPF framework with free functions and parameters to model the transition between large, intermediate, and small scales in modified gravity theories.

Findings

PPF accurately describes f(R) and DGP models.

Framework enables consistency tests of gravity theories.

Suppression of modifications in halos is necessary for local tests.

Abstract

We develop a parameterized post-Friedmann (PPF) framework which describes three regimes of modified gravity models that accelerate the expansion without dark energy. On large scales, the evolution of scalar metric and density perturbations must be compatible with the expansion history defined by distance measures. On intermediate scales in the linear regime, they form a scalar-tensor theory with a modified Poisson equation. On small scales in dark matter halos such as our own galaxy, modifications must be suppressed in order to satisfy stringent local tests of general relativity. We describe these regimes with three free functions and two parameters: the relationship between the two metric fluctuations, the large and intermediate scale relationships to density fluctuations and the two scales of the transitions between the regimes. We also clarify the formal equivalence of modified gravity and generalized dark energy. The PPF description of linear fluctuation in f(R) modified action and the Dvali-Gabadadze-Porrati braneworld models show excellent agreement with explicit calculations. Lacking cosmological simulations of these models, our non-linear halo-model description remains an ansatz but one that enables well-motivated consistency tests of general relativity. The required suppression of modifications within dark matter halos suggests that the linear and weakly non-linear regimes are better suited for making complementary test of general relativity than the deeply non-linear regime.