Hints for a Geon from Causal Dynamic Triangulations

TL;DR

The paper investigates whether geon-like self-bound gravitons can manifest as gauge-invariant excitations in four-dimensional CDT by analyzing curvature-based correlators. It constructs normalized correlators $D_{OO}(\tau,s)$ from a dual triangulation and quantum Ricci curvature $Q$, anchored in cosmological time $\tau$, and searches for massive, universal behavior across operators $O\in\{1,Q,Q^2\}$. The results show an intermediate-distance exponential decay with a common mass scale $m$ for both $\Delta Q\Delta Q$ and $\Delta Q^2\Delta Q^2$, suggesting a geon with Planck-scale mass; the mass is robust across operator choices and volumes but increases during rapid cosmological expansion. Together, these findings provide a first nonperturbative signature of geon-like states in CDT and hint at possible connections to dark matter or primordial black holes, while underscoring the exploratory nature and need for further systematic checks.

Abstract

The existence of geons, physical states of self-bound gravitons, has long been proposed. In the context of four-dimensional causal dynamical triangulation simulations we investigate this possibility by measuring curvature-curvature correlators of different gravitational operators. We find a behavior consistent with a massive state, independent of the operators considered, over a certain distance window. While at most a hint, this is tantalizing due to its possible implications for dark matter or (primordial) black holes. We also find indications that the phase of rapid expansion of the obtained de Sitter universe impacts the mass, and relates to quantum fluctuations of space-time.

Figures (4)

• Figure 1: Global properties as a function of cosmological time. The extent in simplices is measured by the cube root of all simplices with a vertex on a given fat time slice. Error bars are smaller than the plot points.
• Figure 2: The inverse correlation function for $O=1$ with fits of type $a+b\cosh(m(s-s_0))$. It is shown for three cosmological times, which can be compared to figure \ref{['global']}: $\tau=0$ (blue) is the largest extent, $\tau=22$ (orange) is the inflection point of the $Q$ change, and $\tau=32$ (red) is the point where the system settles on the smallest extent. The perpendicular lines give the size at the corresponding $\tau$ in terms of the cube root of simplices, for illustration of the relative sizes.
• Figure 3: The normalized correlation function for $O=\Delta Q$ with fits of type $a+b\exp(-ms)$ and their $\pm1\sigma$ error band (top panel) at $\tau=0$. The same for the $O=R$, extracted using (\ref{['ricci']}) for each measurement of pairs (bottom panel). The fit fixes the same mass as in the top panel, and only determines $a$ and $b$. We note that the first two points in distance could be affected by discretization errors, and therefore deviate from an exponential.
• Figure 4: The extracted mass from the normalized correlators of $O=\Delta Q$ and $O=\Delta Q^2$.