关于变$c^2$项全息暗能量的一个注记
A note on holographic dark energy with varying $c^2$ term
摘要：
我们重新考虑了在能量密度中引入慢时变$ c^2(z)$参数的全息暗能量（HDE）模型，即$ρ_D=3M_p^2 c^2(z)/L^2$，其中$L$是红外截止，$z$是红移参数.作为系统的IR截止，我们选择哈勃半径和Granda-Oliveros（GO）截止。后者的灵感来自Ricci标量曲率。我们导出了宇宙学参数如状态方程和减速参数的演化作为红移参数$z$的显函数。然后，我们绘制了这些宇宙学参数在宇宙历史中的红移参数的演变。有趣的是，我们观察到，通过选择$L=H^{-1}$作为具有时变$ c ^2(z) $项的HDE的IR截止，即使在没有暗能量和暗物质之间的相互作用的情况下，也可以实现宇宙膨胀的加速。这与通常的HDE模型不同，当红外截止点取为哈勃半径时，常$c^2$项会导致错误的状态方程，即尘埃$w_D=0$的状态方程。
英文摘要：
We reconsider the holographic dark energy (HDE) model with a slowly time varying $ c^2(z)$ parameter in the energy density, namely $ρ_D=3M_p^2 c^2(z)/L^2$, where $L$ is the IR cutoff and $z$ is the redshift parameter. As the system's IR cutoff we choose the Hubble radius and the Granda-Oliveros (GO) cutoffs. The latter inspired by the Ricci scalar curvature. We derive the evolution of the cosmological parameters such as the equation of state and the deceleration parameters as the explicit functions of the redshift parameter $z$. Then, we plot the evolutions of these cosmological parameters in terms of the redshift parameter during the history of the universe. Interestingly enough, we observe that by choosing $L=H^{-1}$ as the IR cutoff for the HDE with time varying $ c ^2(z) $ term, the present acceleration of the universe expansion can be achieved, even in the absence of interaction between dark energy and dark matter. This is in contrast to the usual HDE model with constant $c^2$ term, which leads to a wrong equation of state, namely that for dust $w_D=0$, when the IR cutoff is chosen the Hubble radius.
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