Arrow of time in a recollapsing quantum universe

Abstract

We argue that the Wheeler-DeWitt equation with a consistent boundary condition is only compatible with an arrow of time that formally reverses in a recollapsing universe. To recover a classically recollapsing universe in terms of wave packets, we impose the usual boundary condition of excluding exponentially increasing wave functions for large scale factors. Consistency of these opposite arrows is then facilitated by quantum effects in the region of the classical turning point. We also discuss in this context the meaning of the time-asymmetric expression used in the definition of ‘‘consistent histories.’’ Since gravitational time dilation diverges at horizons, one has to conclude that collapsing matter must start reexpanding ‘‘anticausally’’ (controlled by the reversed arrow) in this scenario before horizons or singularities can form. There would then also be no mass inflation nor any information loss paradox.