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 present-day dark energy density was taken to be ρq ≡ 3α 2m2P /η , where η is the conformal time and α 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 Ω q ≃ 0.73 and the equation of state parameter w q < −0.78, if the numerical constant α takes a reasonably large value, α & 2.6. However, in the presence of a nontrivial gravitational coupling of q-field to matter, say e Q, the model may be adjusted to the values Ω q ≃ 0.73 and w q ≃ −1, even if α ∼ O(1), given that the present value of e Q is large. Unlike for the model in [R.G. Cai, arXiv:0707.4049], the bound Ω q < 0.1 during big bang nucleosynthesis (BBN) may be satisfied for almost any value of α. 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. PACS numbers: 95.36.+x, 98.80.Es