Semiclassical Universe from First Principles

Abstract

Causal Dynamical Triangulations in four dimensions provide a background-independent definition of the sum over space-time geometries in nonperturbative quantum gravity. We show that the macroscopic four-dimensional world which emerges in the Euclidean sector of this theory is a bounce which satisfies a semiclassical equation. After integrating out all degrees of freedom except for a global scale factor, we obtain the ground state wave function of the universe as a function of this scale factor.

Figures (4)

• Figure 1: Monte Carlo snapshot of a "typical universe" of discrete volume 91.100 four-simplices and total time extent (vertical direction) $t=40$. The circumference at integer proper time $s$ is proportional to the spatial three-volume $V_3(s)$. The surface represents an interpolation between adjacent spatial volumes, without capturing the actual 4d connectivity between neighbouring spatial slices.
• Figure 2: Measurement of spatial volume-volume correlator for space-times with 22.250, 45.500, 91.000, 181.000 and 362.000 four-simplices, plotted as function of the scaled variable $x=\Delta/V_4^{1/4}$.
• Figure 3: Distribution $P_{V_3}(z)$ of volume differences of adjacent spatial slices, for three-volumes $V_3=$ 10.000, 20.000, 40.000 and 80.000 tetrahedra.
• Figure 4: The potential $V(a)$ of (\ref{['3.3']}) underlying the standard minisuperspace dynamics (left) and the analogous potential in the effective action obtained from the full quantum gravity model, with small-$a$ modification due to quantum fluctuations (right).