"Expansion" around the vacuum equation of state - sudden future singularities and asymptotic behavior

Abstract

The dark energy model with the equation of state p_d=-rho_d - A rho_d^alpha is studied. The model comprises and provides realization of several types of singularities in different parameter regimes: the divergence of the dark energy density and pressure at finite time and finite value of the scale factor, the singularity of the "big rip" type and the sudden future singularity recently introduced by Barrow. For parameter choices which lead to a nonsingular expansion of the universe, various types of the asymptotic evolution are found. The entire time evolution of the universe is described both analytically and numerically. The advantages of this dark energy EOS as a parametrization of dark energy are discussed.

Figures (8)

• Figure 1: The time evolution of the scale factor of the universe for $\Omega_{d,0}=0.7$, $\Omega_{m,0}=0.3$, $\tilde{A} = 1$ and four typical values of the parameter $\alpha$: $\alpha = -1,0.5,0.75,2$. For $\alpha=2$, the scale factor reaches the finite value at the singularity while for $\alpha=0.75$, the scale factor of the universe diverges at singularity.
• Figure 2: The time dependence of the Hubble parameter for $\tilde{A} = 1$, $\Omega_{d,0}=0.7$, $\Omega_{m,0}=0.3$, and $\alpha = -1,0.5,0.75,2$. For $\alpha=0.75$ and $\alpha = 2$ there is the singularity of the Hubble parameter appearing at finite time.
• Figure 3: The time evolution of the dark energy density for $\tilde{A} =1$, $\Omega_{d,0}=0.7$, $\Omega_{m,0}=0.3$, and the typical values $\alpha= -1,0.5,0.75,2$. For $\alpha=0.75$ and $\alpha = 2$, there is the onset of singularity of the dark energy density at finite time.
• Figure 4: The time dependence of the dark energy pressure for $\tilde{A} = 1$, $\Omega_{d,0}=0.7$, $\Omega_{m,0}=0.3$, and the typical values $\alpha= -1,0.5,0.75,2$. For $\alpha=0.75$ and $\alpha = 2$, the dark energy pressure diverges to $-\infty$.
• Figure 5: The time evolution of the scale factor of the universe for $\Omega_{d,0}=0.7$, $\Omega_{m,0}=0.3$, $\tilde{A}=-0.5$ and $\alpha=-1$. The scale factor of the universe is finite at the onset of singularity.