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/a(n)(t) integral(t)(0) dt' a(m) (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 w(m), we have w(de) similar or equal to -1 - 2n/3 for n >= 0 and m m >= 0. The models with n > m >= 0 become single-parameter models like the Lambda CDM model due to the analytic feature Omega(de) similar or equal to d(2)/4(2m + 3w(m) + 3)(2)a(2(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 Omega(de) 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 proportional to 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 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 [1] is the most favorable model and compatible with the Lambda CDM model.