Dark Energy and the Fate of the Universe

TL;DR

The paper argues that a future global collapse is a generic outcome for a broad class of dark-energy models, not limited to supergravity, whenever the scalar potential allows $V(\phi) < 0$ or is unbounded below. Through analyses of M-theory contexts (compactification and non-compactification), two-field $N=8$ models, and a general potential framework, it shows that inflation-like acceleration can be followed by rapid collapse with $t_{\rm collapse}$ of order $t_0$. By constructing near-viable models with small negative offsets, such as $V(\phi)=\Lambda_C\left(e^{-\lambda\phi}-C\right)$, the authors demonstrate that present acceleration can coexist with collapse within $10^{10}$–$10^{11}$ years, depending on $C$, and that observations can constrain the collapse timescale. The work emphasizes a testable link between the microphysics of dark energy and the ultimate fate of the universe, urging observational bounds on $t_{\rm collapse}$ and slow-roll conditions $|m^2| \lesssim H^2$.

Abstract

It is often assumed that in the course of the evolution of the universe, the dark energy either vanishes or becomes a positive constant. However, recently it was shown that in many models based on supergravity, the dark energy eventually becomes negative and the universe collapses within the time comparable to the present age of the universe. We will show that this conclusion is not limited to the models based on supergravity: In many models describing the present stage of acceleration of the universe, the dark energy eventually becomes negative, which triggers the collapse of the universe within the time t = 10^10-10^11 years. The theories of this type have certain distinguishing features that can be tested by cosmological observations.

Figures (6)

• Figure 1: Scale factor $a(t)$ in the model based on $N=8$ supergravity. The upper (red) curve corresponds to the model with $\phi_0 = 0$. In this case the universe can stay at the top of the effective potential for an extremely long time, until it becomes destabilized by quantum effects Kallosh:2001gr. The curves below it correspond to $\phi_0 = 0.2$ and $\phi_0 = 0.3$. The blue dashed curve corresponds to $\phi_{0} = 0.35$. The present moment is $t=0$. Time is given in units of $H^{-1}(t=0) \approx 14$ billion years.
• Figure 2: Effective potential $V = \Lambda_C\left(e^{\phi/2}-C\right)$ with $C= 0,\, 0.1\ ,0.2,\, 0.3$ and $0.4$. The coefficients $\Lambda_C$ are fixed by the condition that for each value of $C$ one should have the same value of the Hubble constant and $\Omega_D=0.7$ at the present moment $t=t_0$.
• Figure 3: Scale factor $a(t)$ in the model with the potential $V = \Lambda_C\left(e^{\phi/2}-C\right)$. The upper (red) curve corresponds to the model with $C = 0$. The curves below it correspond to $C= 0.1,\, 0.2,\, 0.3$ and $0.4$. The present moment is $t=0$. Time is given in units of $H^{-1}(t=0) \approx 14$ billion years.
• Figure 4: Dark energy $\Omega_D$ as a function of redshift $z$ for $V = \Lambda_C\left(e^{\phi/2}-C\right)$ with $C= 0,\, 0.1,\, 0.2,\, 0.3$ and $0.4$. The present time corresponds to $z=0$. As we see, all curves are practically indistinguishable, except for the dashed curve corresponding to $C= 0.3$.
• Figure 5: Equation of state $w$ as a function of redshift $z$ for $C= 0,\, 0.1,\,0.2,\, 0.3$ and $0.4$. For $C= 0.4$ this function sharply rises to $w >0$ near $z=0$. The red (thick) line $w =-1$ corresponds to the model with $C = 0$.