Remarks on dynamical dark energy measured by the conformal age of the universe

We elaborate on a model of conformal dark energy (dynamical dark energy measured by the conformal age of the universe) recently proposed in [H. Wei and R. G. Cai, arXiv:0708.0884] where the presentday dark energy density was taken to be rho(q)equivalent to 3 alpha(2)m(P)(2)/eta(2), where eta is the conformal time and alpha is a numerical constant. In the absence of an interaction between the ordinary matter and dark energy field q, the model may be adjusted to the present values of the dark energy density fraction Omega(q)similar or equal to 0.73 and the equation of state parameter w(q)<-0.78, if the numerical constant alpha takes a reasonably large value, alpha greater than or similar to 2.6. However, in the presence of a nontrivial gravitational coupling of q-field to matter, say Q, the model may be adjusted to the values Omega(q)similar or equal to 0.73 and w(q)similar or equal to-1, even if alpha similar to O(1), given that the present value of Q is large. Unlike for the model in [R. G. Cai, arXiv:0707.4049], the bound Omega(q)< 0.1 during big bang nucleosynthesis (BBN) may be satisfied for almost any value of alpha. Here we discuss some other limitations of this proposal as a viable dark energy model. The model draws some parallels with the holographic dark energy; we also briefly comment on the latter model.