ABSTRACT

In this note , we propose a new model of agegraphic dark energy based on the Károlyházy relation , where the time scale is chosen to be the conformal time \eta of the Friedmann-Robertson-Walker ( FRW ) universe .
We find that in the radiation-dominated epoch , the equation-of-state parameter of the new agegraphic dark energy w _ { q } = -1 / 3 whereas \Omega _ { q } = n ^ { 2 } a ^ { 2 } ; in the matter-dominated epoch , w _ { q } = -2 / 3 whereas \Omega _ { q } = n ^ { 2 } a ^ { 2 } / 4 ; eventually , the new agegraphic dark energy dominates ; in the late time w _ { q } \to - 1 when a \to \infty , and the new agegraphic dark energy mimics a cosmological constant .
In every stage , all things are consistent .
The confusion in the original agegraphic dark energy model proposed in arXiv:0707.4049 disappears in this new model .
Furthermore , \Omega _ { q } \ll 1 is naturally satisfied in both radiation-dominated and matter-dominated epochs where a \ll 1 .
In addition , we further extend the new agegraphic dark energy model by including the interaction between the new agegraphic dark energy and background matter .
In this case , we find that w _ { q } can cross the phantom divide .