A note on agegraphic dark energy

Recently a new model of dynamical dark energy, or time-varying Λ, was proposed by Cai [R.G. Cai, Phys. Lett. B 657 (2007) 228, arXiv:0707.4049 [hep-th]] by relating the energy density of quantum fluctuations in a Minkowski space-time, namely ρq≡3n2mP2/t2, where n∼O(1) and t is the cosmic time, to the present day dark energy density. In this note, we show that the model can be adjusted to the present values of dark energy density parameter Ωq (≃0.73) and the equation of state wq (≃ − 1) only if the numerical coefficient n takes a reasonably large value (n≳3) or the present value of the gravitational coupling of q-field to (dark) matter is also nonzero, namely, Q˜≃2n(Ωq0)3/2>0 where Ωq0 is the present value of dark energy density fraction. We also discuss some of the difficulties of this proposal as a viable dark energy model with a constant n; especially, the bound imposed on the dark energy density parameter Ωq<0.1 during big bang nucleosynthesis (BBN) requires n<1/6. To overcome this drawback, we outline a few modifications where such constraints can be weakened or relaxed. Finally, by establishing a correspondence between the agegraphic dark energy scenario and the standard scalar-field model, we also point out some interesting features of an agegraphic quintessence model.