Reconstructing the Universe

TL;DR

This work demonstrates that a nonperturbative quantum gravity theory defined via causal dynamical triangulations yields a large-scale four-dimensional spacetime with semiclassical volume dynamics, while exhibiting highly nonclassical microstructure. By performing extensive Monte Carlo simulations at fixed four-volume, the authors show four-dimensional global scaling (D_H ≈ 4) and a scale-dependent spectral dimension that flows from D_S(0) ≈ 2 to D_S(∞) ≈ 4, indicating a dynamically generated ultraviolet cutoff. An effective Euclidean action for the scale factor is extracted, matching the minisuperspace form up to a sign flip in the kinetic term, thereby resolving conformal-instability concerns in the Euclidean sector. The analysis of spatial slices reveals a rich nonclassical geometry—thin slices resemble branched polymers with D_S ≈ 1.56 and d_H ≈ 3, while thick slices exhibit D_H ≈ 4 and D_S ≈ 2 with suppressed baby universes—pointing to a nuanced, scale-dependent quantum geometry with potential analytic bridges to branched-polymer models and quantum cosmology.

Abstract

We provide detailed evidence for the claim that nonperturbative quantum gravity, defined through state sums of causal triangulated geometries, possesses a large-scale limit in which the dimension of spacetime is four and the dynamics of the volume of the universe behaves semiclassically. This is a first step in reconstructing the universe from a dynamical principle at the Planck scale, and at the same time provides a nontrivial consistency check of the method of causal dynamical triangulations. A closer look at the quantum geometry reveals a number of highly nonclassical aspects, including a dynamical reduction of spacetime to two dimensions on short scales and a fractal structure of slices of constant time.

Figures (20)

• Figure 1: The two fundamental building blocks of causal dynamically triangulated gravity. The flat four-simplex of type (4,1) on the left has four of its vertices at time $\tau$ and one at time $\tau\!+\! 1$, and analogously for the (3,2)-simplex on the right. The "gap" between two consecutive spatial slices of constant integer time is filled by copies of these simplicial building blocks and their time-reversed counterparts, the (1,4)- and the (2,3)-simplices.
• Figure 2: Unnormalized distribution of the number $N_4^{(3,2)}$ of four-dimensional simplices of type (3,2), at fixed numbers of four-simplices of type (4,1), for $N_4^{(4,1)}=$ 40, 80 and 160k (left to right) at $\kappa_0\!=\! 2.2$ and $\Delta\!=\! 0.6$.
• Figure 3: A qualitative sketch of the phase diagram of four-dimensional causal dynamical triangulations as function of the gravitational coupling $\kappa_0$ and the asymmetry parameter $\Delta$.
• Figure 4: Monte Carlo snapshot of a typical universe in phase A ($\kappa_0\!=\! 5.0$, $\Delta\!=\! 0$), of discrete volume $N_4\!=\!$ 45.5k and total time extent (vertical direction) $t\!=\! 20$. In this and the following two figures, the circumference at integer proper time $\tau$ is chosen proportional to the spatial three-volume $V_3(\tau)$. The surface represents an interpolation between adjacent spatial volumes, without capturing the actual 4d connectivity between neighbouring spatial slices.
• Figure 5: Monte Carlo snapshot of a typical universe in phase B ($\kappa_0\!=\! 1.6$), of discrete volume $N_4\!=\!$ 22.25k and total time extent $t\!=\! 20$. The entire universe has collapsed into a slice of minimal time extension.