Observational Bounds on Cosmic Doomsday

TL;DR

This work examines whether the future lifetime of the universe can be bounded within a simple dark-energy framework featuring a linear potential $V(\phi)=V_0(1+\alpha\phi)$. By solving the scalar-field dynamics and employing a Fisher-matrix forecast for SNAP, Planck, and weak lensing data, the authors translate constraints on the dark-energy equation of state, parameterized as $w(z)=w_0+w_a(1-a)$, into bounds on the doomsday time $t_c$ when $V(\phi)$ becomes negative and the universe collapses. They find current data imply $t_c>\sim10$ Gyr, while upcoming observations could push this bound to $t_c>\sim40$ Gyr (95% CL), with even tighter limits when multiple probes are combined; the exact bound shifts only modestly with moderate changes in $\Omega_D^0$. The results underscore that even a cosmological-constant–like behavior does not guarantee eternal acceleration, and identifying any time variation in $w(z)$ would have profound implications for the universe’s fate and future observational strategy.

Abstract

Recently it was found, in a broad class of models, that the dark energy density may change its sign during the evolution of the universe. This may lead to a global collapse of the universe within the time t_c ~ 10^{10}-10^{11} years. Our goal is to find what bounds on the future lifetime of the universe can be placed by the next generation of cosmological observations. As an example, we investigate the simplest model of dark energy with a linear potential V(φ) =V_0(1+αφ). This model can describe the present stage of acceleration of the universe if αis small enough. However, eventually the field φrolls down, V(φ) becomes negative, and the universe collapses. The existing observational data indicate that the universe described by this model will collapse not earlier than t_c > 10 billion years from the present moment. We show that the data from SNAP and Planck satellites may extend the bound on the "doomsday" time to t_c > 40 billion years at the 95% confidence level.

Figures (6)

• Figure 1: Scale factor $a(t)$ in five models, the present moment is $t=0$. The upper (red) curve corresponds to the cosmological constant model with the vanishing slope $\alpha$; classically it has an infinite future lifetime. The curves below (orange, purple, blue, and black) correspond to a steepening slope. The time remaining from today to the future collapse in these models is shown in the table. Time is given in units of $H^{-1}_0 \approx 13.7/0.983$ billions of years. In these units the current age of the universe $t \approx 13.7$ Gyr is given by $0.983$.
• Figure 2: Evolution of dark energy equation of state $w(z)$ in five models; the present moment is at $z=0$. The value $w(0)$ is also given in the table.
• Figure 3: Dependence of the lifetime of the universe (starting from the present moment), in units of $H_0^{-1}$) on $\alpha$ in the linear model.
• Figure 4: Confidence contours for different combinations of data sets are plotted assuming a fiducial cosmological constant ($w_0=-1$, $w_a=0$) model. The innermost, orange (dashed) ellipse represents SNAP[SN] + Planck + SNAP[WL] at 95% (68%) confidence level. The slightly wider purple ellipses use only SNAP[SN] + Planck, and the rounder, blue ellipses use only SNAP[SN].
• Figure 5: Saturn plot of Fisher ellipses: Each of the Fisher ellipses shown in Fig. \ref{['star72v1']} is now given for fiducial $\Omega_D^0$ taking 3 values: $0.70, 0.72, 0.73$. The innermost ellipse in each case corresponds to $\Omega_D^0= 0.73$, the outermost one corresponds to $\Omega_D^0= 0.70$.