The Semiclassical Limit of Causal Dynamical Triangulations

TL;DR

The paper investigates the nonperturbative semiclassical limit of causal dynamical triangulations (CDT) and tests whether the emergent macroscopic geometry matches Euclidean de Sitter space. It introduces a Gaussian-volume-fix scheme to control fluctuations and extracts the effective action for the three-volume from covariance data, confirming the de Sitter profile and revealing short-distance discretization effects. It further refines the spatial slicing to reveal universal volume behavior across integer and half-integer time layers, supporting a robust semiclassical limit. It finds evidence for a curvature-corrected effective action with a nonzero xi_2 term but without clear scaling to a surviving $R^2$ term in the continuum, underscoring the nonperturbative nature of CDT and the need for improved access to the UV regime.

Abstract

Previous work has shown that the macroscopic structure of the theory of quantum gravity defined by causal dynamical triangulations (CDT) is compatible with that of a de Sitter universe. After emphasizing the strictly nonperturbative nature of this semiclassical limit we present a detailed study of the three-volume data, which allows us to re-confirm the de Sitter structure, exhibit short-distance discretization effects, and make a first detailed investigation of the presence of higher-order curvature terms in the effective action for the scale factor. Technically, we make use of a novel way of fixing the total four-volume in the simulations.

Figures (8)

• Figure 1: Example of a volume distribution $N(n)$ for a specific path-integral configuration (red), compared to the average distribution $\langle N(n)\rangle$ (blue). On the scale of the plot, the latter cannot be distinguished from a fit to the theoretical curve of relation (\ref{['sphere']}).
• Figure 2: Top: probability distribution ${\cal P}_n(N)$ of three-volumes at fixed time $n=29$; bottom: probability distribution ${\cal P}_n(N)$ in the stalk (for every $n\leq 17$); the data fall into three families (colour-coded in the graph), each one with a different behaviour.
• Figure 3: The probability distribution $P_{22}(N)$ from the transition region near the end of the blob. For small $N$ the distribution splits into 3 families (top). For large $N$ the split disappears, but the distribution is highly asymmetric (bottom, no colour-coding for the three families).
• Figure 4: The averaged distributions $\left\langle N(n) \right\rangle$ and $\left\langle N\left(n + \frac{1}{2}\right) \right\rangle$ combine into a single curve after performing a suitable relative rescaling.
• Figure 5: Combining the averaged volume distributions $\left\langle N\left(n\right) \right\rangle$, $\left\langle N\left(n + \frac{1}{3}\right) \right\rangle$ and $\left\langle N\left(n + \frac{2}{3}\right) \right\rangle$ into a single one.