Some comments are made on the usefulness or otherwise of the concept of `expanding space in cosmology. These notes are an expanded version of material first published in 2001 but not previously available online except at www.roe.ac.uk/japwww. Since t
hat personal webpage has been referred to in published work, it seems sensible to give these notes a more permanent home.
It has been claimed that the observed magnitude of the vacuum energy density is consistent with the distribution predicted in anthropic models, in which an ensemble of universes is assumed. This calculation is revisited, without making the assumption
that the CMB temperature is known, and considering in detail the possibility of a recollapsing universe. New accurate approximations for the growth of perturbations and the mass function of dark haloes are presented. Structure forms readily in the recollapsing phase of a model with negative Lambda, so collapse fraction alone cannot forbid Lambda from being large and negative. A negative Lambda is disfavoured only if we assume that formation of observers can be neglected once the recollapsing universe has heated to T > 8 K. For the case of positive Lambda, however, the current universe does occupy a extremely typical position compared to the predicted distribution on the Lambda-T plane. Contrasting conclusions can be reached if anthropic arguments are applied to the curvature of the universe, and we discuss the falsifiability of this mode of anthropic reasoning.
