An account of the arrow of time when scale is surplus

Abstract: Existing accounts of the cosmological arrow of time face a dilemma: generalist approaches that posit time-asymmetric laws lack independent motivation, while particularist approaches that invoke a Past Hypothesis face serious conceptual and explanatory problems. We propose a novel account that dispenses with the need for both time-asymmetric laws and a Past Hypothesis. Instead, it is centred around a symmetry argument that reveals attractors and so-called 'Janus points'. The main idea is that the global spatial scale of the Universe is not empirically accessible, and should therefore be treated as surplus structure. By contrast, the Hubble parameter, which encodes the relative rate of change of scale, is empirically accessible. Once the scale redundancy is eliminated, the empirically meaningful description of cosmic dynamics involves a drag-like variable that transforms in a way that preserves time-reversal invariance. The resulting space of dynamical possibilities possesses universal attractors and Janus points, giving rise to particular states in which observers experience a cosmological arrow of time akin to our own. We illustrate the proposal by applying it to cosmological and gravitational N-body models, showing how it accounts, respectively, for the rapid cooling of the early universe and its relative smoothness.