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Bouncing Cosmologies: Progress and Problems

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Abstract

We review the status of bouncing cosmologies as alternatives to cosmological inflation for providing a description of the very early universe, and a source for the cosmological perturbations which are observed today. We focus on the motivation for considering bouncing cosmologies, the origin of fluctuations in these models, and the challenges which various implementations face.

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Notes

  1. For critical views on how inflation addresses the flatness and entropy problems the reader is referred to [6, 7] and [8,9,10] respectively.

  2. We shall not here consider those mixed models in which a contracting phase followed by a bounce leads to an inflationary era. Such models enjoy the benefits of both paradigms, but also imply a higher level of sophistication which, at the present time, may not be required by the data; Occam’s razor demands they should be introduced only at a later stage if needed.

  3. Not all cosmologists accept that inflation is predictive, citing the “multiverse” issue as a problem [52]—but see [53] for another view on this issue.

  4. Here we are using a convention for the Fourier transform in which the Fourier modes have mass dimension \(-3/2\) plus the mass dimension of the position space quantity.

  5. It should be noted that in [139], a regular scalar field was used in conjunction with positive spatial curvature to avoid the primordial singularity through a bounce: a special state was assumed, with very large occupation number, that was leading to a direct violation of the NEC.

  6. In this subsection we use the convention that the mass dimension of \(\zeta (k)\) is \(-3\) and not \(-3/2\) as we did earlier in this review.

  7. Models of inflation based on matter which violates the NEC can yield a blue spectrum, see e.g. [247].

  8. For an elaboration on this point, see [54].

  9. Note that a similar problem arises during reheating in inflationary cosmology.

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Acknowledgements

One of the authors (RB) wishes to thank the Institute for Theoretical Studies of the ETH Zürich for kind hospitality. He acknowledges financial support from Dr. Max Rössler, the Walter Haefner Foundation and the ETH Zurich Foundation, and from a Simons Foundation fellowship. The research of RB is also supported in part by funds from NSERC and the Canada Research Chair program. PP would like to thank the Labex Institut Lagrange de Paris (Reference ANR-10-LABX-63) part of the Idex SUPER, within which this work has been partly done.

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Authors and Affiliations

  1. Physics Department, McGill University, Montreal, QC, H3A 2T8, Canada

    Robert Brandenberger

  2. Institute for Theoretical Studies, ETH Zürich, 8092, Zürich, Switzerland

    Robert Brandenberger

  3. Institut d’Astrophysique de Paris, UMR 7095, 98 Bis Boulevard Arago, 75014, Paris, France

    Patrick Peter

  4. Institut Lagrange de Paris, 98 Bis Boulevard Arago, 75014, Paris, France

    Patrick Peter

  5. UPMC Université Paris 6 et CNRS, Sorbonne Universités, Paris, France

    Patrick Peter

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Brandenberger, R., Peter, P. Bouncing Cosmologies: Progress and Problems. Found Phys 47, 797–850 (2017). https://doi.org/10.1007/s10701-016-0057-0

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