Phase profile of the wave function of canonical tensor model and emergence of large spacetimes

TL;DR

This paper investigates the phase profile of the wave function in the canonical tensor model of quantum gravity, revealing how large spacetimes and their growth emerge through saddle point analysis and numerical simulations.

Contribution

It provides the first detailed analysis of the wave function's phase profile in coordinate space, demonstrating emergent large spacetimes and growth dynamics in the canonical tensor model.

Findings

Lie group symmetric spacetimes are strongly favored due to saddle points

Spatial sizes grow over 'time' as indicated by phase profiles

Monte Carlo simulations confirm saddle point results and reveal light mode disturbances

Abstract

To understand spacetime dynamics in the canonical tensor model of quantum gravity for the positive cosmological constant case, we analytically and numerically study the phase profile of its exact wave function in a coordinate representation, instead of the momentum representation analyzed so far. A saddle point analysis shows that Lie group symmetric spacetimes are strongly favored due to abundance of continuously existing saddle points, giving an emergent fluid picture. The phase profile suggests that spatial sizes grow in "time", where sizes are measured by the tensor-geometry correspondence previously introduced using tensor rank decomposition. Monte Carlo simulations are also performed for a few small $N$ cases by applying a re-weighting procedure to an oscillatory integral which expresses the wave function. The results agree well with the saddle point analysis, but the phase profile is subject to disturbances in a large spacetime region, suggesting existence of light modes there and motivating future computations of primordial fluctuations from the perspective of canonical tensor model.