Analysis on a general class of holographic type dark energy models

We present a detail analysis on a general class of holographic type dark energy models characterized by the length scale L = 1/an(t)∫0tdt' am(t'). We show that n ≥ 0 is required by the recent cosmic accelerated expansion of universe. In the early universe dominated by the constituent with constant equation of state wm, we have wde ≅ −1−2n/3 for n ≥ 0 and m < 0, and wde ≅ −(2/3)(n−m)+wm for n > m ≥ 0. The models with n > m ≥ 0 become single-parameter models like the ΛCDM model due to the analytic feature Ωde ≅ d2/4(2m+3wm+3)2a2(n−m) at radiation- and matter-dominated epoch. Whereas the cases n = m ≥ 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 ≥ 0 are forbidden by the self-consistent requirement Ωde << 1 in the early universe. Thus a detailed study on the single-parameter models corresponding to cases n > m ≥ 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∝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 wde < −1 during inflation to wde > −1 in radiation- and matter-dominated epoch, and then back to wde < −1 eventually. The best-fit result of the case (n = 0, m = −1) which is so-called ηHDE model proposed in (Huang 2012) is the most favorable model and compatible with the ΛCDM model