XIIth School of Cosmology
September 15 - 20, 2014IESC, Cargèse
their impact in the study of galaxies and

Bouncing universe models

Patrick PETER
Institut d'Astrophysique de Paris (IAP)


  1. Overview of bouncing models
    • Ekpyrotic and cyclic scenarios
    • Non singular models in string theory
    • Singular models
    • Model zoology
  2. Requirements for a successful bounce
    • Cosmological puzzle resolution
    • The question of shear & the BKL instability
    • The ekpyrotic phase
  3. Cosmological perturbations in the bouncing case
    • Viability of perturbations in a contracting universe
    • A scale-invariant spectrum?
    • Tensor-to-scalar ratio
    • Non gaussianities
  4. A worked-out model
    • Quantum cosmology, Wheeler De Witt and the minisuperspace
    • Bouncing perfect fluid cosmology
    • Perturbations & predictions for the observations.


Alternative to inflationary cosmology have been proposed over the years that almost all involve, in one form or another, a phase of contraction followed by a bounce connecting to our currently expanding universe. These models often need to face theoretical difficulties and predict observable consequences at odd with the available data. In these lectures, I will present the necessary ingredients of a working alternative-to-inflation model, discuss their implementation in terms of field or string theory and examine the above mentioned difficulties. I will try and expose some recent ideas based on quantum cosmology within the framework of which a more satisfactory construction could be done.


  • Articles
    • "The Matter Bounce Alternative to Inflationary Cosmology"
      R. H. Brandenberger - arXiv:1206.4196
    • "Cosmology without inflation"
      P. Peter & N. Pinto-Neto, Phys. Rev. D 78, 063506 (2008) - arXiv:0809.2022
    • "Primordial cosmology"
      P. Peter & J.-P. Uzan, - Oxford University Press (2013)