Analysis on a General Class of Holographic Type Dark Energy Models

Abstract

We present a detail analysis on a general class of holographic type dark energy models characterized by the length scale $L=\frac{1}{a^n(t)}{\int }_0^{t}d{t}^{\prime }{a}^m(t^{\prime })$. We show that $n\ge 0$ is required by the recent cosmic accelerated expansion of universe. In the early universe dominated by the constituent with constant equation of state $w_m$, we have $w_{de}\simeq -1-\frac{2n}{3}$ for $n\ge 0$ and $m<0$, and $w_{de}\simeq -\frac{2}{3}(n-m)+w_m$ for $n>m\ge 0$. The models with $n>m\ge 0$ become single-parameter models like the $\Lambda$CDM model due to the analytic feature ${\Omega }_{de}\simeq \frac{d^2}{4}(2m+3w_m+3{)}^2{a}^{2(n-m)}$ at radiation- and matter-dominated epoch. Whereas the cases $n=m\ge 0$ should be abandoned as the dark energy cannot dominate the universe forever and there might be too large fraction of dark energy in early universe, and the cases $m>n\ge 0$ are forbidden by the self-consistent requirement ${\Omega }_{de}\ll 1$ in the early universe. Thus a detailed study on the single-parameter models corresponding to cases $n>m\ge 0$ is carried out by using recent observations. The best-fit analysis indicates that the conformal-age-like models with $n=m+1$, i.e. $L\propto \frac{1}{Ha}$ in early universe, are more favored and also the models with smaller $n$ for the given $n-m$ are found to fit the observations better. The equation of state of the dark energy in models with $n=m+1>0$ transits from $w_{de}<-1$ during inflation to $w_{de}>-1$ in radiation- and matter-dominated epoch, and then back to $w_{de}<-1$ eventually. The best-fit result of the case $(n=0,m=-1)$ which is so-called $\eta$HDE model proposed in \cite{Huang:2012xm} is the most favorable model and compatible with the $\Lambda$CDM model.

20 pages, 5 figures, minor typos corrected, reference added, published version in JCAP

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