Kolmogorov complexity in the Milky Way and its reduction with warm dark matter

Abstract

We discuss the Kolmogorov complexity of primordial patches that collapse to form galaxies like the Milky Way; this complexity quantifies the amount of initial data available to form the structure. We also speculate on how the quantity changes with time. Because of dark-matter and baryonic collapse processes, it likely decreases with time, i.e.\ information sinks dominate sources. But sources of new random information do exist; e.g., a central black hole with an accretion disk and jets could in principle broadcast small-scale quantum fluctuations over a substantial portion of a galaxy. A speculative example of how this concept might be useful is in differentiating between warm (WDM) and cold (CDM) dark matter. With WDM, the initial patch that formed the Milky Way would have had few features, making the present high degree of structure a curiosity. The primordial patch would have had only several billion independent information-carrying `pixels' if the WDM particle had a mass of 1 keV. This number of `pixels' is much less than even the number of stars in the Milky Way. If the dark matter is proven to be warm, the high degree of structure in the Milky Way could have arisen in two ways: (1) from a high sensitivity to initial conditions, like an intricate fractal arising from a relatively simple computer code; or (2) from random information generated after the galaxy formed, i.e.\ not entirely deterministically from the initial conditions.