Expanding and Self-Organizing 2D Universe Models Emerging from Frozen Trivalent Spin Networks

TL;DR

This paper explores self-organized criticality in extended trivalent spin network models, demonstrating that different stochastic growth schemes can produce expanding dual spaces with power-law or exponential behaviors, relevant to quantum gravity.

Contribution

It introduces new stochastic growth schemes in TSN models that lead to critical states and space expansion without fine-tuning, broadening understanding of emergent spacetime in LQG.

Findings

Power-law avalanche size distributions observed.

Two classes of space evolution: power-law correlations and loitering phases.

Expansion of dual spaces occurs without fine-tuning.

Abstract

We revisit the topic of self-organized criticality (SOC) in simple statistical graph models, with the purpose of capturing essential processes leading to the emergence of macroscopic spacetime from the microscopic dynamics in loop quantum gravity (LQG). We performed a large set of simulations based on extensions of the frozen trivalent spin network (TSN) model explored previously by Ansari and Smolin. Their model mimicked the sandpile dynamics by the application of random vertex propagation rules in the TSN, leading to a SOC behavior in the distribution of the avalanche sizes, as well as a slowly expanding, $2$-dimensional dual (triangulated) space. Here we show that a growth scheme for the stochastic, slow external driving force, differing from the classical sandpile model, also resulted in power-law distributed avalanche sizes. Our simulations also produced expanding dual spaces, with two basic classes of evolution: one with power-law correlations in "space" and "time", and the other with "loitering" and exponential phases. Our work expands the range of models in which critical states in the TSN may lead to expansion effects in the dual space, without fine-tuning.