Assumptions of Randomness in Cosmology Models

TL;DR

This paper explores the limitations of randomness assumptions in cosmological models, especially regarding non-compact symmetries and the implications for observer placement, proposing topological solutions and discussing algorithmic randomness complexities.

Contribution

It introduces the use of pointed spaces to address randomness issues in infinite cosmology models and discusses the algorithmic complexity of randomness in sequences.

Findings

Non-compact symmetries lack invariant probability distributions.

Pointed spaces can circumvent randomness issues in cosmology.

Randomized algorithms can produce uncomputable sequences not equivalent to random ones.

Abstract

Non-compact symmetries cannot be fully broken by randomness since non-compact groups have no invariant probability distributions. In particular, this makes trickier the "Copernican" random choice of the place of the observer in infinite cosmology models. This problem may be circumvented with what topologists call pointed spaces. Then randomness will be used only in building (infinite) models around the pre-designated "observation point", that thus would not need to be randomly chosen. Additional complications come from the original randomness possibly being hidden. P. Gacs and A. Kucera proved that every sequence can be algorithmically generated from a random one. But Vladimir V'yugin discovered that randomized algorithms can with positive probability generate uncomputable sequences that are not algorithmically equivalent to any random ones.