Holographic Dark Energy Model Characterized by the Conformal-age-like
  Length
  A holographic dark energy model characterized by the conformal-age-like
length scale $L= \frac{1}{a^4(t)}\int_0^tdt' a^3(t') $ is motivated from the
four dimensional spacetime volume at cosmic time $t$ in the flat
Friedmann-Robertson-Walker universe. It is shown that when the background
constituent with constant equation of state $w_m$ dominates the universe in the
early time, the fractional energy density of the dark energy scales as
$\Omega_{de}\simeq \frac94(3+w_m)^2d^2a^2$ with the equation of state given by
$w_{de}\simeq-\frac23 +w_m$. The value of $w_m$ is taken to be $w_m\simeq-1$
during inflation, $w_m=\frac13$ in radiation-dominated epoch and $w_m=0$ in
matter-dominated epoch respectively. When the model parameter $d$ takes the
normal value at order one, the fractional density of dark energy is naturally
negligible in the early universe, $\Omega_{de} \ll 1$ at $a \ll 1$. With such
an analytic feature, the model can be regarded as a single-parameter model like
the $\Lambda$CDM model, so that the present fractional energy density
$\Omega_{de}(a=1)$ can solely be determined by solving the differential
equation of $\Omega_{de}$ once $d$ is given. We further extend the model to the
general case in which both matter and radiation are present. The scenario
involving possible interaction between the dark energy and the background
constituent is also discussed.
