We present a best-fit analysis on the single-parameter holographic dark energy model characterized by the conformal-age-like length , L = \frac { 1 } { a ^ { 4 } ( t ) } \int _ { 0 } ^ { t } dt ^ { \prime } ~ { } a ^ { 3 } ( t ^ { \prime } ) .
Based on the Union2 compilation of 557 supernova Ia data , the baryon acoustic oscillation results from the SDSS DR7 and the cosmic microwave background radiation data from the WMAP7 , we show that the model gives the minimal \chi ^ { 2 } _ { min } = 546.273 , which is comparable to \chi ^ { 2 } _ { \Lambda { CDM } } = 544.616 for the \Lambda CDM model .
The single parameter d concerned in the model is found to be d = 0.232 \pm 0.006 \pm 0.009 .
Since the fractional density of dark energy \Omega _ { de } \sim d ^ { 2 } a ^ { 2 } at a \ll 1 , the fraction of dark energy is naturally negligible in the early universe , \Omega _ { de } \ll 1 at a \ll 1 .
The resulting constraints on the present fractional energy density of matter and the equation of state are \Omega _ { m 0 } = 0.286 ^ { +0.019 } _ { -0.018 } ~ { } ^ { +0.032 } { } _ { -0.028 } and w _ { de 0 } = -1.240 ^ { +0.027 } _ { -0.027 } ~ { } ^ { +0.045 } { } _ { -0.044 } respectively .
The model leads to a slightly larger fraction of matter comparing to the \Lambda CDM model .
We also provide a systematic analysis on the cosmic evolutions of the fractional energy density of dark energy , the equation of state of dark energy , the deceleration parameter and the statefinder .
It is noticed that the equation of state crosses from w _ { de } > -1 to w _ { de } < -1 , the universe transits from decelerated expansion ( q > 0 ) to accelerated expansion ( q < 0 ) recently , and the statefinder may serve as a sensitive diagnostic to distinguish the CHDE model with the \Lambda CDM model .