Advertisement

The equations of Conformal Cyclic Cosmology

  • Paul TodEmail author
Research Article

Abstract

I review the equations of Conformal Cyclic Cosmology given by Penrose (Cycles of time: an extraordinary new view of the universe. Bodley Head, London, 2010). Motivated by the example of FRW cosmologies, I suggest a slight modification to Penrose’s prescription and show how this works out for Class A Bianchi cosmologies, and in general.

Keywords

Cosmological models Conformal geometry 

References

  1. 1.
    Anderson, M.T.: Canonical metrics on 3-manifolds and 4-manifolds. Asian J. Math. 10, 127–163 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    Anguige, K.: Isotropic cosmological singularities. III. The Cauchy problem for the inhomogeneous conformal Einstein–Vlasov equations. Ann. Phys. 282, 395–419 (2000)CrossRefADSzbMATHMathSciNetGoogle Scholar
  3. 3.
    Anguige, K., Tod, K.P.: Isotropic cosmological singularities. I. Polytropic perfect fluid spacetimes. Ann. Phys. 276, 257–293 (1999)CrossRefADSzbMATHMathSciNetGoogle Scholar
  4. 4.
    Anguige, K., Tod, K.P.: Isotropic cosmological singularities. II. The Einstein–Vlasov system. Ann. Phys. 276, 294–320 (1999)CrossRefADSzbMATHMathSciNetGoogle Scholar
  5. 5.
    Fefferman, C., Graham, C.R.: The Ambient Metric. Annals of Mathematics Studies, vol. 178. Princeton University Press, Princeton (2012)Google Scholar
  6. 6.
    Friedrich, H.: On purely radiative space-times. Commun. Math. Phys. 103, 35–65 (1986)CrossRefADSzbMATHMathSciNetGoogle Scholar
  7. 7.
    Friedrich, H.: On the global existence and the asymptotic behavior of solutions to the Einstein–Maxwell–Yang–Mills equations. J. Differ. Geom. 34, 275–345 (1991)zbMATHMathSciNetGoogle Scholar
  8. 8.
    Lee, J.M., Parker, T.H.: The Yamabe problem. Bull. Am. Math. Soc. 17, 37–91 (1987)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Lübbe, C.: Conformal scalar fields, isotropic singularities and conformal cyclic cosmologies. arXiv:1312.2059
  10. 10.
    Lübbe, C., Kroon, J.A.V.: A conformal approach for the analysis of the non-linear stability of radiation cosmologies. Ann. Phys. 328, 1–25 (2013)CrossRefADSzbMATHGoogle Scholar
  11. 11.
    Newman, E.T.: A Fundamental Solution to the CCC equation. arXiv:1309.7271
  12. 12.
    Penrose, R.: Cycles of Time: An Extraordinary New View of the Universe. Bodley Head, London (2010)Google Scholar
  13. 13.
    Penrose, R., Rindler, W.: Spinors and Space-Time, Volume 1: Two-Spinor Calculus and Relativistic fields. Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge (1987)Google Scholar
  14. 14.
    Rendall, A.D.: Asymptotics of solutions of the Einstein equations with positive cosmological constant. Ann. Henri Poincar 5, 1041–1064 (2004)CrossRefADSzbMATHMathSciNetGoogle Scholar
  15. 15.
    Starobinsky, A.A.: Isotropization of arbitrary cosmological expansion given an effective cosmological constant. JETP Lett. 37, 66–69 (1983)ADSGoogle Scholar
  16. 16.
    Tod, K.P.: Isotropic cosmological singularities in spatially homogeneous models with a cosmological constant. Class. Quantum Grav. 24, 2415–2432 (2007)CrossRefADSzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

Personalised recommendations