1. ^*Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
2. ^†Department of Physics, University of California, Irvine, California 92717, USA

Abstract

Petrosian¹ has recently discussed the possibility that the restoration of symmetry at grand unification in a closed contracting Robertson–Walker universe could slow down and halt the contraction, causing the universe to bounce. He then went on to discuss the possibility that our universe has undergone a series of such bounces. We disagree with this analysis. One of us (M.S.) has already shown² that if a contracting universe is dominated by radiation, then a bounce is impossible. We will show here two further results: (1) entropy considerations imply that the quantity S (defined in ref. 1 and below), which must decrease by 10⁷⁵ to allow the present Universe to bounce, can in fact decrease by no more than a factor of 2; (2) if the true vacuum state has zero energy density, then a universe which is contracting in its low temperature phase can never complete a phase transition soon enough to cause a bounce.