Since the HDE model is obtained by choosing the event horizon length-scale, an obvious drawback concerning causality appears in this scenario. Recently, a new DE model, dubbed agegraphic dark energy (ADE) model, has been suggested by Cai (2007) in order to alleviate the above problem. In particular, combining the uncertainty principle in quantum mechanics and the gravitational effects of GR Karolyhazy and his collaborators (Karolyhazy 1966; Karolyhazy & Lukacs 1982, 1986) made an interesting observation concerning the distance measurement for the Minkowski space–time through a light-clock Gedanken experiment (see also Maziashvili 2007a). They found that the distance t in Minkowski space–time cannot be known to a better accuracy than $\delta t=\beta t_{\rm p}^{2/3}t^{1/3}$, where β is a dimensionless constant of the order of ${\cal O}(1)$ (see also Maziashvili 2007a).1 Based on the Karolyhazy relation, Maziashvili (2007a) argued that the energy density of metric fluctuations in the Minkowski space–time is written as (see also Maziashvili 2007b)

(2)

\begin{equation}
\rho _{{\rm d}}\sim \frac{1}{t_{{\rm p}}^{2}t^{2}}\sim \frac{m_{{\rm p}}}{t^{2}},
\end{equation}

where mp and tp are the reduced Plank mass and the Plank time, respectively (see also Ng & Van Dam 1994, 1995; Sasakura 1999; Krauss & Turner 2004; Christiansen, Ng & van Dam 2006; Arzano, Kephart & Ng 2007; Ng 2007). Using equation (2), Cai (2007) proposed another version of holographic DE, the so-called ADE, in which the time-scale t is chosen to be equal with the age of the universe $T= \int ^{t}_0{\rm d}t=\int _{0}^{a}\frac{{\rm d}a}{aH}$, with a the scalefactor of the universe and H the Hubble parameter. Therefore, the ADE energy density is given by (Cai 2007)

(3)

\begin{equation}
\rho _{{\rm d}}=\frac{3n^{2}m_{{\rm p}}^{2}}{T^{2}},
\end{equation}

where n is a free parameter and the coefficient 3 appears for convenience. The present value of the age of universe ($T_{\rm 0}\sim H_{\rm 0}^{-1}$) implies that n is of the order of ${\cal O}(1)$. It has been shown that the condition n > 1 is required in order to have cosmic acceleration (Cai 2007). Although, the ADE scenario does not suffer from the causality problem (Cai 2007), it faces some problems towards describing the matter-dominated epoch (Neupane 2007; Wei & Cai 2008a,b). To overcome this issue, Wei & Cai (2008a) proposed a new agegraphic dark energy (NADE) model, in which the cosmic time t is replaced by the conformal time $\eta = \int ^{t}_0{\frac{{\rm d}t}{a(t)}}=\int ^{a}_0{\frac{{\rm d}a}{a^{2}H}}$ and thus the energy density in this case becomes (Wei & Cai 2008a)

(4)

\begin{equation}
\rho _{{\rm d}}=\frac{3n^{2}m_{{\rm p}}^{2}}{\eta ^{2}}.
\end{equation}

It is interesting to mention that Kim, Lee & Myung (2008b) showed that the NADE model provides the proper matter-dominated and radiation-dominated epochs, in the case of n > 2.68 and n > 2.51, respectively. Also, Wei & Cai (2008b) found that the coincidence problem can be alleviated naturally in this model and using the cosmological data (SNIa, CMB, etc.), they obtained $n=2.716^{+0.111}_{-0.109}$. We would like to point out that the cosmological properties of the ADE and the NADE models can be found in Kim et al. (2008a), Setare & Jamil (2011), Karami et al. (2011), Sheykhi & Setare (2010), Sheykhi (2009), Sheykhi (2010a), Sheykhi (2010b), Sheykhi (2010c), Lee, Kim & Myung (2008), Jawad, Chattopadhyay & Pasqua (2013), Liu et al. (2012), Zhang, Li & Zhang (2013), Farajollahi, Ravanpak & Fadakar (2012), Zhai, Zhang & Liu (2011), Chen et al. (2011), Sun & Yue (2011), Lemets, Yerokhin & Zazunov (2011), Zhang, Zhang & Zhang (2010), Liu, Zhang & Zhang (2010), Karami & Khaledian (2011), Malekjani & Khodam-Mohammadi (2010), Jamil & Saridakis (2010), Karami et al. (2010), Sheykhi (2010a), Sheykhi (2010b), Sheykhi (2009), Wu, Ma & Ling (2008), Zhang, Zhang & Liu (2008), Kim et al. (2008b), Neupane (2009) and Wei & Cai (2008b).
Citation: Cai (2007)
Citation function: Background; Background
Citation: Cai (2007)
Citation function: Background; Background
Citation: Cai 2007
Citation function: Uses; Uses
Citation: Cai 2007
Citation function: Compare/Contrast; Compare/Contrast