Parametrized 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.

The Vainshtein mechanism in the cosmic web

“…The values of r c are tuned so that these models have correspondence with the f (R) model of Ref. [41] (Hu-Sawicki) in terms of σ 8 . Specifically, nDGP1, 2, and 3 have the same σ 8 as the Hu-Sawicki model with |f R0 | = 10 −4 , 10 −5 , and 10 −6 , respectively.…”

Tests of modified gravity with dwarf galaxies

“…For all f (R) models α = 1/ √ 6, and the numerator ϕ b /2α ≈ f R0 where f R0 is a parameter commonly used in the literature to constrain the model (Hu & Sawicki 2007). The strongest constraints from large-scale structure come from cluster abundances and set an upper limit of f R0 ≈ 10 −4 (Schmidt et al 2009;Lombriser et al 2010).…”

Cusp singularities in f(R) gravity:prosandcons

“…For some dark energy models, e.g., Starobinsky model [8] and Hu-Sawicki model [9], gravitational collapses can trigger to create a cusp singularity.…”

“…In this paper, we are especially interested in four models: the Starobinsky (dark energy) model [8], the Hu-Sawicki model [9], and their cured forms by adding ∼ R 2 corrections. a. Starobinsky model The Starobinsky (dark energy) model is as follows [8]:…”

“…In order to obtain a stable and non-vanishing (de Sitter) local minimum, one often has to fabricate the shape of the effective potential of the Brans-Dicke field; equivalently, one has to tune a form of f (R) [8,9]. For this, the R −n (n > 0) corrections have often been introduced, which nevertheless become the origin of the trouble.…”