Supergravity, Dark Energy and the Fate of the Universe

TL;DR

The paper investigates whether dark energy and cosmic acceleration can be realized within extended supergravity frameworks, focusing on de Sitter solutions and the characteristic mass–Hubble relations m^2 = n H_0^2. It combines analysis of N≥2 gauged supergravities (including N=8,M-theory-related models) with explicit numerical cosmologies, as well as simple N=1 constructions (Polónyi, axion) and exponential potentials, to show that most dS vacua are unstable and lead to a future collapse on timescales comparable to the current age, while a minority yield true future de Sitter expansion. The work emphasizes that ultra-light scalar fields with |m| ~ H_0 provide a natural, quantum-stable link between microphysics and late-time cosmology, and discusses observational signatures that could distinguish collapsing versus eternally accelerating universes. It also connects M-theory and STU/axion-dilaton sectors to realistic dark-energy phenomenology, highlighting potential tensions with event horizons in string theory and the role of initial conditions in determining fate.

Abstract

We propose a description of dark energy and acceleration of the universe in extended supergravities with de Sitter (dS) solutions. Some of them are related to M-theory with non-compact internal spaces. Masses of ultra-light scalars in these models are quantized in units of the Hubble constant: m^2 = n H^2. If dS solution corresponds to a minimum of the effective potential, the universe eventually becomes dS space. If dS solution corresponds to a maximum or a saddle point, which is the case in all known models based on N=8 supergravity, the flat universe eventually stops accelerating and collapses to a singularity. We show that in these models, as well as in the simplest models of dark energy based on N=1 supergravity, the typical time remaining before the global collapse is comparable to the present age of the universe, t = O(10^{10}) years. We discuss the possibility of distinguishing between various models and finding our destiny using cosmological observations.

Figures (13)

• 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: Dark energy $\Omega_D$ as a function of redshift $z$ for $\phi_{0}= 0,\, 0.2,\, 0.3 ,\, 0.35$. The lower (red) curve corresponds to the model with $\phi_0 = 0$. The present time corresponds to $z=0$. Note that for $\phi_{0}= 0.35$ the maximal value of $\Omega_D$ is about 0.65.
• Figure 3: Equation of state function $w$ as a function of redshift $z$ for $\phi_{0}= 0,\, 0.2,\, 0.3 ,\, 0.35$. For $\phi_{0}= 0.35$ this function sharply rises near $z=0$. For $\phi_{0}= 0.3$ the maximal value of $w$ is about $-0.65$. This could also seem too high, but the average value of $w$ in the important interval $z\lesssim 2$ is below $-0.9$. For $\phi_{0}= 0.2$ the maximal value of $w$ is below $-0.9$. The red line $w =-1$ corresponds to the model with $\phi_0 = 0$.
• Figure 4: Scale factor $a(t)$ in the model based on $N=2$ supergravity with a stable dS minimum for $\phi_{0}= 0,\, 0.6,\, 1.0,\, 10$. The upper (red) line corresponds to $\phi_0 = 0$, the lower (blue) line corresponds to $\phi_0 = 10$. Blue lines in this figure and in the next two figures practically coincide with the corresponding lines for the purely exponential potential $V \sim e^{\sqrt 2 \phi}$.
• Figure 5: Dark energy $\Omega_D(z)$ for $\phi_{0}= 0,\, 0.6,\, 1.0,\, 10$. The lower (red) line corresponds to $\phi_0 = 0$, the upper (blue) line corresponds to $\phi_0 = 10$.