Remarks on Dynamical Dark Energy Measured by the Conformal Age of the Universe

Abstract

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 $ρ_q \equiv 3 α^2 m_P^2/η^2$, 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 $Ω\Z{q} \simeq 0.73$ and the equation of state parameter $w\Z{q} < -0.78$, if the numerical constant $α$ takes a reasonably large value, $α\gtrsim 2.6$. However, in the presence of a nontrivial gravitational coupling of $q$-field to matter, say $\widetilde{Q}$, the model may be adjusted to the values $Ω\Z{q}\simeq 0.73$ and $w\Z{q}\simeq -1$, even if $α\sim {\cal O}(1)$, given that the present value of $\widetilde{Q}$ is large. Unlike for the model in [R.G. Cai, arXiv:0707.4049], the bound $Ω\Z{q} <0.1$ 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.