Canf(R)modified gravity theories mimic aΛCDMcosmology?

Abstract

We consider f (R) modified gravity theories in the metric variation formalism and attempt to reconstruct the function f (R) by demanding a background ΛCDM cosmology. In particular we impose the following requirements: a. A background cosmic history H(z) provided by the usual flat ΛCDM parametrization though the radiation (w ef f = 1/3), matter (w ef f = 0) and deSitter (w ef f = −1) eras. b. Matter and radiation dominate during the 'matter' and 'radiation' eras respectively i.e. Ωm = 1 when w ef f = 0 and Ωr = 1 when w ef f = 1/3. We have found that the cosmological dynamical system constrained to obey the ΛCDM cosmic history has four critical points in each era which correspondingly lead to four forms of f (R). One of them is the usual general relativistic form f (R) = R − 2Λ. The other three forms in each era, reproduce the ΛCDM cosmic history but they do not satisfy requirement b. stated above.

Dark energy from modified F(R)-scalar-Gauss–Bonnet gravity

“…The corresponding classes of scalar potentials may be easily constructed (see an explicit example of such construction in the Appendix). It is interesting that in such unified model it is easier to realize the known classical universe history ( radiation/matter dominance, decceleration-acceleration transition, cosmic acceleration) than in pure F (R) gravity [7,8] or in pure scalar-GB gravity [14,15]. There is no problem to take into account usual matter in such consideration.…”

“…As clear from (6) or (8), the expressions of V (φ) and ξ 1 (φ) depend on the explicit form of F (R), say µ in (9), and the time-development of the universe g(t), nowH 0 andH 1 , (and f (φ) in case of (6)). Then the form of F (R) is irrelevant to the WMAP data but only g(t) is relevant as long as we use the expressions in (6) or (8).…”

“…Recently, big number of works was devoted to the study of late-time cosmology and solar system tests checks in modified F (R) gravity [5,6]. While it is not easy to satisfy all known solar system tests at once, it is possible to construct the explicit models [7,8] which describe the realistic universe expansion history (radiation/matter dominance, transition to acceleration and accelerating era).…”

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

“…The addition of a non-linear function of the Ricci scalar R to the Einstein-Hilbert action has been demonstrated to cause acceleration for a wide variety of f (R) functions [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,…”

Unifying inflation with ΛCDM epoch in modified f(R) gravity consistent with Solar System tests

“…It is expected that modified gravity (for a review, see [1]) approach which may be related with string/M-theory [2] may help in the understanding of the dark energy origin. For instance, various modified f (R) gravities have been constructed and applied to the description of the late-time cosmic acceleration [3,4,5,6,7,8] with also the check of local tests. Even the form of modified f (R) gravity may be reconstructed from the known universe expansion history [9].…”