We propose a new type of cosmological model in which it is postulated thatnot only the temperature but also the curvature is limited by the mass scale ofthe Hagedorn temperature. We find that the big bang of this universe issmoothly connected to the big crunch of the previous universe through aHagedorn universe, in which the temperature and curvature remain very close totheir limiting values. In this way, we obtain the picture of a cyclic universe.By estimating the entropy gained in each big crunch and big bang, we reach theconclusion that our universe has repeated this process about forty times afterit was created at the Planck scale. We also show that the model gives ascale-invariant spectrum of curvature perturbations.
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