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

By Luca Amendola, R. Gannouji, D. Polarski, S. Tsujikawa. 2006

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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 of studying the m(r) curve on the (r,m) plane, where m{identical_to}Rf{sub ,RR}/f{sub ,R} and r{identical_to}-Rf{sub ,R}/f with f{sub ,R}{identical_to}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_equal}+0 and dm/dr>-1 at r{approx_equal}-1. For the existence of a viable late-time acceleration we require instead either (i) m=-r-1, ({radical}(3)-1)/2 0 and n<-1 and are thus cosmologically unacceptable. Similarmore » 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{proportional_to}t{sup 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.« less

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/92a03689b7a5917296c514547994b14d20e32ec5

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Citations in the corpus

Modified Gravity and Cosmology (2011, background): “This has been done for the case of a number of particular f(R) theories in [248, 310, 790, 5, 538] and also in the general case in [390, 306, 40, 253].”
Curing singularities in cosmological evolution of F(R) gravity (2009, background): “However, in the case of F (R) models of present DE, the necessity to keep it valid for all values of R during the matter- and radiation-dominated stages in order to avoid the Dolgov-Kawasaki instability [13] has been realized rather recently [14, 15].”
On the Evolution of the Hubble Constant with the SNe Ia Pantheon Sample and Baryon Acoustic Oscillations: A Feasibility Study for GRB-Cosmology in 2030 (2022, methodology): “the Hu-Sawicki [303], the Starobinsky [304], and Tsujikawa models [305,306], successfully describe the Dark Energy component (say an effective parameter for the Dark Energy w = w(z) < −1/3) and overcome all local constraints.”