Dark energy model with higher derivative of Hubble parameter

In this letter we consider a dark energy model in which the energy density is a function of the Hubble parameter $H$ and its derivative with respect to time $ρ_{de}=3α\ddot{H}H^{-1}+3β\dot{H}+3γH^2$. The behavior of the dark energy and the expansion history of the Universe depend heavily on the parameters of the model $α$, $β$ and $γ$. It is very interesting that the age problem of the well-known three old objects can be alleviated in this models.

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