Avoiding recollapse in an open-AdS Universe via a self-tuning-like mechanism

Abstract

We study whether an open FLRW Universe with a negative cosmological constant can evade the eventual recollapse characteristic of AdS-type Universe. Within a power-law realization of Fab-Four theory, we solve the background equations numerically and analyze the asymptotic dynamics. We find that the scalar sector provides a self-tuning-like compensation of the negative Λ while leaving the spatial-curvature term unscreened. Consequently, the expansion does not reverse. Instead, the Universe evolves toward a curvature-dominated linear-expansion regime, a {\propto} t. To probe the underlying compensation mechanism, we further analyze an auxiliary zero-curvature subsystem using Poincaré compactification. The physically admissible trajectories approach a critical point at infinity where the compensating scalar-Λ sector becomes stiff-like (w_{φ+Λ} {\to} 1), so that its effective energy density redshifts faster than curvature (w_k = -1/3). Although this auxiliary analysis does not cover the full curved cosmology, it is consistent with and qualitatively supports the numerical finding that the net φ + Λ contribution becomes subdominant to curvature, thereby preventing recollapse despite Λ < 0. This extends the application of the self-tuning mechanism to the AdS region and offers a possibility for the AdS Universe predicted by string theory to become a reality.

Figures (2)

• Figure 1: Evolution of the AdS vacua with and without $\phi$. In the upper panel, the horizontal axis denotes cosmic time, while the vertical axis represents the scale factor. The red curve corresponds to the evolution of the AdS vacua, whereas the blue curve shows the evolution after additional scalar field $\phi$. The lower panel displays the evolution of the energy densities of different components. Since a negative $\Lambda$ contributes a negative energy density, absolute values are taken for some quantities for the purpose of clearer visualization, as indicated in the legend. We numerically obtained the above results using Eq. \ref{['Fun:F11']} and Eq. \ref{['Fun:Motivation Function']}. The initial conditions for AdS with $\phi$ are $p=0,\;\phi_0=1,\; \dot{\phi}_0=-0.001,\; a_0=1,\; \dot{a}_0=1,\;\alpha_i=1,\; k=-5/3,\; \Lambda=-2.016$. For the case without $\phi$, the initial conditions are $p=0,\; a_0=1,\; \dot{a}_0=1,\;\alpha_i=1,\; k=-5/3,\; \Lambda=-2$. The speed of light and gravitational constant are set $G=1,\ c=1$.
• Figure 2: Phase of the dynamical system under different projections, for $\alpha_1=\alpha_2=\alpha_4=1$. The upper-left panel shows the phase portrait on the $x_1$--$x_2$ plane, the lower-left panel shows the projection of the Poincaré sphere along the polar direction, and the right panel illustrates the asymptotic behavior as $x_2\to\infty$. The curves denote trajectories with different initial conditions, and the arrows indicate the direction of evolution; the same initial conditions are used in all projections. The white and gray regions correspond to $\Lambda<0$ and $\Lambda>0$, respectively. Stars mark the finite critical points, while triangles mark the critical points at infinity. The green solid line indicates the singularity of the system, which is omitted in the other panels.