1306.3164 (Hamid Shabani et al.)

f(R,T) Dark Energy Models in Phase Space    [PDF]

Hamid Shabani, Mehrdad Farhoudi

We investigate cosmological solutions of f(R,T) modified theories of gravity for a perfect fluid in a spatially homogeneous and isotropic background through phase space analysis, where R is Ricci scalar and T denotes trace of energy-momentum tensor of matter content. The theory is explored for minimal case f(R,T)=g(R)+h(T), pure non-minimal case f(R,T)=g(R)h(T), and f(R,T)=g(R)+g(R)h(T). For first case, the acceptable cosmological solutions which contain long enough matter dominated era followed by a late-time accelerated expansion are found. We classify solutions in six classes which demonstrate more acceptable solutions than the f(R) gravity. In background of f(R,T) gravity, cosmological behavior of some function g(R) is explored theoretically and is shown that the models $aR^{-\beta}$ for $-1.43\leq\beta<-1$ with $a>0$, $R [\log{(\alpha R)}]^{q}$ for two values $q=\pm1$ with $\alpha>0$, $R^{p}\exp{(qR)}$ for $p\rightarrow 1^{+}$ with $q>0$, $R+\alpha R^{-n}$ for $n\rightarrow-1^{+}$ with $\alpha<0$ and $n\rightarrow-1^{-}$ with $\alpha>0$ and $R^{p}\exp{(q/R)}$ for $p\rightarrow 1^{+}$ and $q<0$ confirm our predictions numerically. We draw the cosmological parameters, i.e. matter densities for dust, radiation and dark energy, corresponding scale factors and the effective equation of state. We illustrate that there is a saddle acceleration era which is a middle era before final stable acceleration de Sitter era for some models. Plots are drawn consistent with present values $\Omega^{\textrm{(m)}}_{0}\simeq0.3$, $\Omega^{\textrm{(DE)}}_{0}\simeq0.7$ and $\Omega^{\textrm{(rad)}}_{0}\simeq 10^{-4}$. The pure non-minimal theory suffers from absence of a standard matter era. Therefore, this model is not interesting from cosmological point of view. Although, we illustrate that theory f(R,T)=g(R)+g(R)h(T) can have acceptable cosmological solutions.

View original: http://arxiv.org/abs/1306.3164