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

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

2000-09-18

arxiv.org/abs/gr-qc/0009063v1

Phys.Rev. D63 (2001) 084026

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, 1 firgure, submitted to Phys. Rev. D

Scientific paper

10.1103/PhysRevD.63.084026

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.

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