A Parameterized Post-Friedmann Framework for Modified Gravity

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.

12 pages, 9 figures, additional references reflect PRD published version

References in corpus (5)

• Models of f(R) Cosmic Acceleration that Evade Solar-System Tests
• Constraining f(R) Gravity as a Scalar Tensor Theory
• Dark Energy versus Modified Gravity
• Constraints on a New Post-General Relativity Cosmological Parameter
• Is Modified Gravity Required by Observations? An Empirical Consistency Test of Dark Energy Models

Cited by in corpus (10)

• Large Scale Structure as a Probe of Gravitational Slip
• Distinguishing Modified Gravity from Dark Energy
• Weak Lensing Probes of Modified Gravity
• Parametrized Post-Friedmann Signatures of Acceleration in the CMB
• Next Generation Redshift Surveys and the Origin of Cosmic Acceleration
• Nonlinear growth in modified gravity theories of dark energy
• A sub-horizon framework for probing the relationship between the cosmological matter distribution and metric perturbations
• The Evolution of Bias - Generalized
• Large Scale Structure Formation of Normal Branch in DGP Brane World Model
• Testing Alternative Theories of Dark Matter with the CMB