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General relativistic self-similar waves that induce an anomalous acceleration into the standard model of cosmology


About this Title

Joel Smoller, Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109 and Blake Temple, Department of Mathematics, University of California, Davis, Davis, California 95616

Publication: Memoirs of the American Mathematical Society
Publication Year: 2012; Volume 218, Number 1025
ISBNs: 978-0-8218-5358-0 (print); 978-0-8218-9012-7 (online)
DOI: http://dx.doi.org/10.1090/S0065-9266-2011-00641-6
Published electronically: November 3, 2011
MSC: Primary 34A05, 76L05, 83F05, 85A40

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Self-similar coordinates for the $k=0$ FRW spacetime
  • Chapter 3. The expanding wave equations
  • Chapter 4. Canonical co-moving coordinates and comparison with the $k \ne 0$ FRW spacetimes
  • Chapter 5. Leading order corrections to the standard model induced by the expanding waves
  • Chapter 6. A foliation of the expanding wave spacetimes into flat spacelike hypersurfaces with modified scale factor $R(t) = t^a$.
  • Chapter 7. Expanding wave corrections to the standard model in approximate co-moving coordinates
  • Chapter 8. Redshift vs luminosity relations and the anomalous acceleration
  • Chapter 9. Appendix: The mirror problem
  • Chapter 10. Concluding remarks

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