On the "renormalization" transformations induced by cycles of expansion and contraction in causal set cosmology

TL;DR

This paper investigates the effects of cosmic expansion and contraction cycles on causal set dynamics, identifying fixed points and basins of attraction within a stochastic renormalization framework.

Contribution

It characterizes the fixed points of the renormalization group induced by cosmic cycles in causal set theory and analyzes their stability and basins of attraction.

Findings

Fixed points correspond to transitive percolation dynamics.

No other fixed points or cycles of length two or more exist.

An extensive basin of attraction is identified, but it does not cover all parameters.

Abstract

We study the ``renormalization group action'' induced by cycles of cosmic expansion and contraction, within the context of a family of stochastic dynamical laws for causal sets derived earlier. We find a line of fixed points corresponding to the dynamics of transitive percolation, and we prove that there exist no other fixed points and no cycles of length two or more. We also identify an extensive ``basin of attraction'' of the fixed points but find that it does not exhaust the full parameter space. Nevertheless, we conjecture that every trajectory is drawn toward the fixed point set in a suitably weakened sense.