M-theory, Cosmological Constant and Anthropic Principle

TL;DR

This work tackles the cosmological constant problem through an anthropic lens anchored in high-energy theory. It argues that inflation creates a multiverse of domains with varying effective constants, and that galaxy-formation and cosmic-age constraints select a narrow range of viable values for the present dark-energy density, narrowing the fine-tuning from ~$10^{120}$ to order unity near $\\rho_0$. The authors embed a de Sitter-like dark-energy sector within maximally extended $d=4$, $N=8$ supergravity, where the small positive cosmological constant arises from a 4-form flux and the vacuum is inherently unstable with a tachyonic mass $m^2=V''(0)=-2\\Lambda=-6H_0^2$. By solving the coupled scalar-gravity dynamics for varying $\\Lambda$ and initial $\\phi_0$, they show that anthropically allowed universes predominantly require $\\Lambda \\sim O(\\rho_0)$ and yield non-negligible probability for $0.5<\\Omega_D<0.9$, offering a potential explanation for the observed coincidence between dark energy and matter densities. The analysis emphasizes that while the precise numbers depend on distributional assumptions, the qualitative picture—an anthropically selected, metastable de Sitter sector tied to M-theory fluxes—remains robust and broadly applicable to related quintessence-inspired frameworks.

Abstract

We discuss the theory of dark energy based on maximally extended supergravity and suggest a possible anthropic explanation of the present value of the cosmological constant and of the observed ratio between dark energy and energy of matter.

Figures (6)

• Figure 1: Evolution of a flat $\Lambda$CDM universe for various values of $\Lambda$. Time is in units of the present age of the universe $t_0 \approx 14$ billion years. The present moment is placed at $t=0$, the big bang corresponds to $t = -1$. The upper (red) line corresponds to the flat universe with $\Omega_{\rm tot} = 1$, $\Omega_\Lambda = 0.7$ (i.e. $\Lambda = +0.7 \rho_0$) and $\Omega_{M} = 0.3$. The next line below it (the blue line) corresponds to a flat universe with $\Lambda = -4.7\rho_0$. As we see, this universe collapses at the age of 14 billion years. The total lifetime of the universe with $\Lambda = -18.8 \rho_0$ (the lower, green line) is only 7 billion years.
• Figure 2: Scalar potential $V(\phi)=\Lambda (2- \cosh {\sqrt 2} \phi)$ in $d=4$$N=8$ supergravity (\ref{['pot']}). The value of the potential is shown in units of $\Lambda$, the field is given in units of $M_p$.
• Figure 3: Expansion of the universe for $\phi_0= 0.25$. Going from right to left, the first (red) line corresponds to $\Lambda = 0.07 \rho_0$, the second (green) line corresponds to $\Lambda = 0.7 \rho_0$, then $\Lambda = 7\rho_0 \ , 70\rho_0$ and $700\rho_0$.
• Figure 4: Expansion of the universe for $\Lambda = 0.7 \rho_0$. The upper (red) line corresponds to the fiducial model with $\phi_0 = 0$ (cosmological constant; field does not move). The (green) line below corresponds to $\phi=0.5$. The next (blue) line corresponds to $\phi = 1$, then to $\phi = 1.5$, and $\phi = 2$.
• Figure 5: The region below the thick (red) line contains all possible $\Lambda$ and $\phi_0$ corresponding to the total lifetime of the universe greater than $14$ billion years. The dashed line $\Lambda \approx 1.5 \rho_0$ separates this region into two equal area parts. The region below the thin (blue) curve corresponds to all universes with the lifetime greater than 28 billion years, i.e. to the universes that would live longer than $14$ billion years after the present moment.