Time Variable Cosmological Constants from the Age of Universe

Abstract

In this paper, time variable cosmological constant, dubbed {\it age cosmological constant}, is investigated motivated by the fact: any cosmological length scale and time scale can introduce a cosmological constant or vacuum energy density into Einstein's theory. The age cosmological constant takes the form $\rho_{\Lambda}=3c^2M^2_P/t_{\Lambda}^2$, where $t_{\Lambda}$ is the age of our universe or conformal time. The effective equation of state of age cosmological constant are $w^{eff}_{\Lambda}=-1+{2/3}\frac{\sqrt{\Omega_{\Lambda}}}{c}$ and $w^{eff}_{\Lambda}=-1+{2/3}\frac{\sqrt{\Omega_{\Lambda}}}{c}(1+z)$ when the age of universe and conformal time are taken as the role of cosmological time scales respectively. They are the same as the so-called agegraphic dark energy models. However, the evolution history are different from the agegraphic ones for their different evolution equations.