Cosmological expansion and the uniqueness of the gravitational action

Abstract

Modified theories of gravity have recently been studied by several authors as possibly viable alternatives to the cosmological concordance model. Such theories attempt to explain the accelerating expansion of the universe by changing the theory of gravity, instead of introducing dark energy. In particular, a class of models based on higher order curvature invariants, so-called f (R) gravity models, has drawn attention. In this letter we show that within this framework, the expansion history of the universe does not uniquely determine the form of the gravitational action and it can be radically different from the standard Einstein-Hilbert action. We demonstrate that for any barotropic fluid, there always exists a class of f (R) models that will have exactly the same expansion history as that arising from the Einstein-Hilbert action. We explicitly show how one can extend the Einstein-Hilbert action by constructing a f (R) theory that is equivalent on the classical level. Due to the classical equivalence between f (R) theories and Einstein-Hilbert gravity with an extra scalar field, one can also hence construct equivalent scalar-tensor theories with standard expansion.

Models off(R)cosmic acceleration that evade solar system tests

“…The deviations peak at ∼ 10 −15 . Such deviations easily pass the stringent solar system tests of gravity from the Cassini mission [95] |γ − 1| < 2.3 × 10 −5 (63) under the assumption that the galactic field f Rg is given by the potential minimum. Models that saturate this observational bound have a sufficiently large |f Rg | that the thin-shell criterion is first satisfied at the edge of the Sun, where the fractional enclosed mass becomes 2M eff /3M tot ≈ 10 −5 (see Eqn.…”

“…What is less clear in the literature is whether any proposed metric-variation f (R) modification can simultaneously satisfy stringent solar-system bounds on deviations from general relativity as well as accelerate the expansion at late times [63,64,65,66,67,68,69,70,71,72,73,74]. Chiba [75] showed that the fundamental difficulty is that f (R) gravity introduces a scalar degree of freedom with the same coupling to matter as gravity that, at the background cosmological density, is extremely light.…”

Dark matter as a geometric effect in f(R)f(R) gravity

“…(36) has been transformed to a first order nonlinear second kind Abel differential equation of the form dw/dθ = A(θ)w 3 +B(θ)w 2 [37]. As it is known from the theory of the Abel differential equations, an equation of this form has an exact solution if and only if the condition d [A(θ)/B(θ)] /dθ = kB(θ) is satisfied, where k is a constant [37].…”

“…For a static and spherically symmetric metric of the form given by Eq. (1), the field equations of the f (R) gravity in vacuum can be expressed as [29,36] …”

Cluster abundance inf(R)gravity models

“…[17] compose a subset of this class. It also has sufficient flexibility to bracket the behavior of models where the combination of a specific expansion history [18,19] and the Compton wavelength today fixes the form of f (R) [20]. For the ΛCDM expansion history and a dimensionless Compton wavelength parameter…”