Fate of an accelerating universe

The presently accelerating universe may keep accelerating forever, eventually run into the event horizon problem, and thus be in conflict with the superstring idea. On the other hand, the current accelerating phase as well as the fate of the universe may be swayed by a negative cosmological constant, which dictates a big crunch. Based on the current observational data, in this paper we investigate how large the magnitude of a negative cosmological constant is allowed to be. In addition, for distinguishing the sign of the cosmological constant via observations, we point out that a measure of the evolution of the dark energy equation-of-state may be a good discriminator. Hopefully future observations will provide much more detailed information about dark energy and thereby indicate the sign of the cosmological constant as well as the fate of the presently accelerating universe.

Figure 1

The plot of $\ln [a(t)/a_0]$, describing the evolution of the universe with ${\rho }_{\Lambda }=-\frac{1}{50}{\rho }_Q(0)$ and that with ${\rho }_{\Lambda }=0$, respectively. The time $t$ is in unit of the Hubble time $H_0^{-1}$ and $t=0$ denotes the present time.

Figure 2

The plot of $H(t)$, describing the evolution of the universe with ${\rho }_{\Lambda }=-\frac{1}{50}{\rho }_Q(0)$ and that with ${\rho }_{\Lambda }=0$, respectively. The time $t$ is in unit of the Hubble time $H_0^{-1}$ and $t=0$ denotes the present time.

Figure 3

The $1\sigma$ constraint on ${\rho }_{\mathrm{DE}}(z)$ (presented by the gray region) and the predictions in various theoretical models which satisfy this constraint (presented by solid curves).

Figure 4

The constraint on $w_{\mathrm{DE}}(0)$ and $w_{\mathrm{DE}}^{\prime }(0)$ (presented by the white region) and the predictions in various theoretical models: $-1.2<w_{\mathrm{x}}<-0.65$ and $\xi \equiv {\Omega }_{\Lambda }/{\Omega }_{\mathrm{x}}>-0.5$ (presented by the black area), which survive this constraint. The gray region is ruled out by SN Ia data, with the prior ${\Omega }_m=0.27\pm 0.04$, at 95% confidence.

Figure 5

The constraint on $w_{\mathrm{DE}}(0)$ and $w_{\mathrm{DE}}^{\prime }(0)$ (presented by the white region) and the predictions in various theoretical models which survive this constraint. The gray region is ruled out by SN Ia data, with the prior ${\Omega }_m=0.27\pm 0.04$, at 95% confidence. The solid curves, from the left to the right side, correspond to theoretical models $\{w_{\mathrm{x}},\xi >{\xi }_m\}$ with $(w_x,{\xi }_m)=(-1.4,-0.12)$, $(-1.3,-0.3)$ , $(-1.2,-0.5)$ , $(-1.1,-0.74)$ , $(-1.01,-0.97)$ , $(-0.99,-0.99)$ , $(-0.9,-0.9)$ , $(-0.8,-0.8)$ , $(-0.7,-0.6)$ , $(-0.6,-0.3)$.