Phase profile of the wave function of canonical tensor model and emergence of large space—times

• Published in: International journal of modern physics. A, Particles and fields, gravitation, cosmology Vol. 36; no. 29
• Main Author: Sasakura, Naoki
• Format: Journal Article
• Language: English
• Published: Singapore World Scientific Publishing Company 20.10.2021; World Scientific Publishing Co. Pte., Ltd
• Subjects: Cosmological constant; Lie groups; Mathematical analysis; Physics; Quantum gravity; Representations; Saddle points; Tensors; Wave functions; canonical formalism; canonical tensor model; Tensor model; ADM formalism; emergent space–time
• ISSN: 0217-751X; 1793-656X
• DOI: 10.1142/S0217751X21502225

In this paper, to understand space–time 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 space–times 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 space–time region, suggesting existence of light modes there and motivating future computations of primordial fluctuations from the perspective of canonical tensor model.