Time variable cosmological constants from the age of universe

Abstract In this Letter, time variable cosmological constant, dubbed 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 ρ Λ = 3 c 2 M P 2 / t Λ 2 , where t Λ is the age or conformal age of our universe. The effective equation of state (EoS) of age cosmological constant are w Λ eff = − 1 + 2 3 Ω Λ c and w Λ eff = − 1 + 2 3 Ω Λ c ( 1 + z ) when the age and conformal age of universe are taken as the role of cosmological time scales respectively. The EoS are the same as the so-called agegraphic dark energy models. However, the evolution histories are different from the agegraphic ones for their different evolution equations.