Conditions for the cosmological viability of f(R) dark energy models

Details Conditions for the cosmological viability of f(R) dark energy models Conditions for the cosmological viability of f(R) dark energy models

2006-12-28

arxiv.org/abs/gr-qc/0612180v2

Phys.Rev.D75:083504,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

25 pages, 11 figures, version to appear in Physical Review D

Scientific paper

10.1103/PhysRevD.75.083504

We derive the conditions under which dark energy models whose Lagrangian densities f are written in terms of the Ricci scalar R are cosmologically viable. We show that the cosmological behavior of f(R) models can be understood by a geometrical approach consisting in studying the m(r) curve on the (r, m) plane, where m=Rf_{,RR}/f_{,R} and r=-Rf_{,R}/f with f_{,R}=df/dR. This allows us to classify the f(R) models into four general classes, depending on the existence of a standard matter epoch and on the final accelerated stage. The existence of a viable matter dominated epoch prior to a late-time acceleration requires that the variable m satisfies the conditions m(r) approx+0 and dm/dr>-1 at r approx-1. For the existence of a viable late-time acceleration we require instead either (i) m=-r-1, (sqrt{3}-1)/20 and n<-1 and are thus cosmologically unacceptable. Similar conclusions can be reached for many other examples discussed in the text. In most cases the standard matter era is replaced by a cosmic expansion with scale factor a propto t^{1/2}. We also find that f(R) models can have a strongly phantom attractor but in this case there is no acceptable matter era.

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