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.
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References
Petrosian, V. Nature 298, 805 (1982).
Sher, M. Phys. Rev. D22, 2989 (1980).
Weinberg, S. Gravitation and Cosmology (Wiley, New York, 1972).
Huang, K. Statistical Mechanics Chs 8, 9 (Wiley, New York, 1963).
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Guth, A., Sher, M. The impossibility of a bouncing universe. Nature 302, 505–506 (1983). https://doi.org/10.1038/302505a0
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DOI: https://doi.org/10.1038/302505a0
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