Are f(R) dark energy models cosmologically viable ?

TL;DR

It is found that, in all f(R) modified gravity theories where a power of R is dominant at large or small R, the scale factor during the matter phase grows as t(1/2) instead of the standard law t(2/3).

Abstract

All $f(R)$ modified gravity theories are conformally identical to models of quintessence in which matter is coupled to dark energy with a strong coupling. This coupling induces a cosmological evolution radically different from standard cosmology. We find that in all $f(R)$ theories that behave as a power of $R$ at large or small $R$ (which include most of those proposed so far in the literature) the scale factor during the matter phase grows as $t^{1/2}$ instead of the standard law $t^{2/3}$. This behaviour is grossly inconsistent with cosmological observations (e.g. WMAP), thereby ruling out these models even if they pass the supernovae test and can escape the local gravity constraints.

Figures (2)

• Figure 1: Evolution of the fractional energy densities ($\phi$, matter, radiation) in EF for the model $f(R)=R-\mu^{4}/R$ (top panel). Overimposed as dotted lines the evolution of $\tilde{\Omega}_{\phi}$ for $n=4$ and $10$. Notice the constant value $\tilde{\Omega}_{\phi}\simeq1/9$ in the $\phi$MDE phase between radiation and DE domination. In the bottom panel we plot the evolution of the observed EOS $w_{\textrm{DE}}$ of DE in JF and the effective EOS in both EF and JF ($n=1$).
• Figure 2: The sound horizon angular distance $\theta_{s}$ as a function of the coupling $\beta$ for $n=1$ (thick line) and $n=-2,3,10$ (dotted lines). The disk marks the value for $\beta=1/2$. The grayed region shows the WMAP3y constraint at $4\sigma$.