Time Variable Cosmological Constants from the Age of Universe

TL;DR

This paper introduces a time-variable cosmological constant based on the universe's age, deriving its properties and comparing it with agegraphic dark energy models, highlighting differences in their evolution histories.

Contribution

It proposes a new age-dependent cosmological constant model and analyzes its effective equation of state, distinguishing it from existing agegraphic dark energy models.

Findings

The effective equation of state depends on the universe's age and conformal time.

The model's evolution differs from traditional agegraphic dark energy.

The proposed model aligns with agegraphic dark energy but exhibits distinct evolution dynamics.

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.