How closed is cosmology?

Classical cosmology exhibits a particular kind of scaling symmetry. The dynamics of the invariants of this symmetry forms a system that exhibits many of the features of open systems such as the non-conservation of mechanical energy and the focusing of measures along the dynamical flow. From these properties, we show that important dynamical features emerge that are not present in closed systems. In particular, a large and physically plausible class of cosmological models give rise to a natural arrow of time. We then argue that the appropriate notion of closure in cosmology is dynamical closure - that a system can be integrated without reference to external factors. This is realised in physical systems in terms of the algebraic closure of the equations of motion such that the system is autonomous. Remarkably, in a growing class of models it can be shown that the autonomous system obtained remains regular and can be integrated through the big bang.