Skip to main content
SpringerLink
Log in

Cosmological Spacetimes Balanced by a Weyl Geometric Scale Covariant Scalar Field

  • Published:
Foundations of Physics Aims and scope Submit manuscript

Abstract

A Weyl geometric approach to cosmology is explored, with a scalar field φ of (scale) weight −1 as crucial ingredient besides classical matter. Its relation to Jordan-Brans-Dicke theory is analyzed; overlap and differences are discussed. The energy-stress tensor of the basic state of the scalar field consists of a vacuum-like term Λg μ ν with Λ depending on the Weylian scale connection and, indirectly, on matter density. For a particularly simple class of Weyl geometric models (called Einstein-Weyl universes) the energy-stress tensor of the φ-field can keep space-time geometries in equilibrium. A short glance at observational data, in particular supernovae Ia (Riess et al. in Astrophys. J. 659:98ff, 2007), shows encouraging empirical properties of these models.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Anderson, J.D., Laing, P.A., Lau, E., Liu, A., Nieto, M., Turyshev, S.: Indication, from Pioneer 10/11, Galileo, and Ulysses data, of an apparent anomalous, weak, long range acceleration. Phys. Rev. Lett. 81, 2858 (1998). arXiv:gr-qc/9808081

    Article  ADS  Google Scholar 

  2. Audretsch, J., Gähler, F., Straumann, N.: Wave fields in Weyl spaces and conditions for the existence of a preferred pseudo-Riemannian structure. Commun. Math. Phys. 95, 41–51 (1984)

    Article  MATH  ADS  Google Scholar 

  3. Bielby, R.M., Shanks, T.: Anomalous SZ contribution to 3 year WMAP data. Mon. Not. R. Astron. Soc. (2007). arXiv:astro-ph/0703470

  4. Brans, C.: The roots of scalar-tensor theories: an approximate history (2004). arXiv:gr-qc0506063

  5. Callan, C., Coleman, S., Jackiw, R.: A new improved energy-momentum tensor. Ann. Phys. 59, 42–73 (1970)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. Canuto, V., Adams, P.J., Hsieh, S.-H., Tsiang, E.: Scale covariant theory of gravitation and astrophysical application. Phys. Rev. D 16, 1643–1663 (1977)

    ADS  MathSciNet  Google Scholar 

  7. Carroll, S.: The cosmological constant. Living Rev. Relativ. 4, 1–77 (2001). Also in arXiv:astro-ph/0004075v2, visited 10 November 2003

    ADS  Google Scholar 

  8. Cartier, P.: La géométrie infinitésimale pure et le boson de Higgs. Talk given at the conference Géométrie au vingtième siècle, 1930–2000, Paris 2001. http://semioweb.msh-paris.fr/mathopales/geoconf2000/videos.asp

  9. Christophe, B., Andersen, P.H., Anderson, J.D.: Odyssee: A solar system mission (2007). arXiv:0711.2007v2 [gr-qc]

  10. Dirac, P.A.M.: Long range forces and broken symmetries. Proc. R. Soc. Lond. A 333, 403–418 (1973)

    ADS  MathSciNet  Google Scholar 

  11. Drechsler, W.: Mass generation by Weyl-symmetry breaking. Found. Phys. 29, 1327–1369 (1999)

    Article  MathSciNet  Google Scholar 

  12. Drechsler, W., Tann, H.: Broken Weyl invariance and the origin of mass. Found. Phys. 29(7), 1023–1064 (1999). arXiv:gr-qc/98020vvv1

    Article  MathSciNet  Google Scholar 

  13. Ellis, G.: 83 years of general relativity and cosmology: progress and problems. Class. Quantum Gravity 16, A43–A75 (1999)

    Article  Google Scholar 

  14. Fahr, H.-J., Heyl, M.: Cosmic vacuum energy decay and creation of cosmic matter. Die Naturwissenschaften 94, 709–724 (2007)

    Article  ADS  Google Scholar 

  15. Faraoni, V.: Cosmology in Scalar-Tensor Gravity. Kluwer, Dordrecht (2004)

    MATH  Google Scholar 

  16. Faraoni, V., Gunzig, E., Nardone, P.: Transformations in classical gravitational theories and in cosmology. Fundam. Cosm. Phys. 20, 121ff (1998). arXiv:gr-qc/9811047

    ADS  Google Scholar 

  17. Folland, G.B.: Weyl manifolds. J. Differ. Geom. 4, 145–153 (1970)

    MATH  MathSciNet  Google Scholar 

  18. Fischer, E.: An equilibrium balance of the universe. Preprint arXiv:0708.3577 (2007)

  19. Fujii, Y., Maeda, K.-C.: The Scalar-Tensor Theory of Gravitation. Cambridge University Press, Cambridge (2003)

    MATH  Google Scholar 

  20. Fulton, T., Rohrlich, F., Witten, L.: Conformal invariance in physics. Rev. Mod. Phys. 34, 442–457 (1962)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. Hasinger, G., Komossa, S.: The X-ray evolving universe: (ionized) absorption and dust, from nearby Seyfert galaxies to high redshift quasars. Report MPE Garching (2007). arXiv:astro-ph/0207321

  22. Hawking, S., Ellis, G.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)

    MATH  Google Scholar 

  23. Hehl, F.W., McCrea, D., Mielke, E., Ne’eman, Y.: Progress in metric-affine gauge theories of gravity with local scale invariance. Found. Phys. 19, 1075–1100 (1989)

    Article  ADS  MathSciNet  Google Scholar 

  24. Hung, C.: Possible existence of Weyl’s vector meson. Phys. Rev. Lett. 61, 2182–2184 (1988)

    Article  ADS  Google Scholar 

  25. Lieu, R.: ΛCDM cosmology: how much suppression of credible evidence, and does the model really lead its competitors, using all evidence? Preprint arXiv:0705.2462 (2007) [astro-ph]

  26. Mannheim, P.: Alternatives to dark matter and dark energy (2005). arXiv:astro-ph/0505266

  27. Mielke, E., Fuchs, B., Schunck, F.: Dark matter halos as Bose-Einstein condensates. In: Proceedings Tenth Marcel Grossmann Meeting, Rio de Janeiro, 2003, pp. 39–58. World Scientific, Singapore (2006)

    Google Scholar 

  28. Myers, A.D., Shanks, T., Outram, P.J., Frith, W.J., Wolfendale, A.W.: Evidence for an extended SZ effect in WMAP data. Mon. Not. R. Astron. Soc. (2004). arXiv:astro-ph/0306180v2

  29. Pawłowski, M., Ra̧czka, R.: A Higgs-free model for fundamental interactions. Part I: Formulation of the model. Preprint ILAS/EP-3-1995 (1995)

  30. Penrose, R.: Zero rest mass fields including gravitation: asymptotic behavior. Proc. R. Soc. Lond. A 284, 159–203 (1965)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  31. Perlmutter, S., Aldering, G., Goldhaber, G., et al.: Measurement of Ω and Λ from 42 high-redshift supernovae. Astrophys. J. 517, 565–586 (1999)

    Article  ADS  Google Scholar 

  32. Quiros, I.: The Weyl anomaly and the nature of the background geometry. Preprint arXiv:gr-qc/0011056 (2000)

  33. Quiros, I.: Transformation of units and world geometry. Preprint arXiv:gr-qc/0004014v3 (2008)

  34. Riess, G.A., Strolger, L.-G., Casertano, S., et al.: New Hubble Space Telescope discoveries of type Ia supernovae at z≥1: Narrowing constraints on the early behavior of dark energy. Astrophys. J. 659, 98ff (2007). arXiv:astro-ph/0611572

    Article  ADS  Google Scholar 

  35. Scholz, E.: On the geometry of cosmological model building. Preprint arXiv:gr-qc/0511113 (2005)

  36. Segal, I.E.: Radiation in the Einstein universe and the cosmic background. Phys. Rev. D 28, 2393–2401 (1983)

    Article  ADS  MathSciNet  Google Scholar 

  37. Shojai, F., Golshani, M.: On the geometrization of Bohmian mechanics: A new approach to quantum gravity. Int. J. Mod. Phys. A 13, 677–693 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  38. Shojai, A.: Quantum, gravity and geometry. Int. J. Mod. Phys. A 15, 1757–1771 (2000)

    MATH  ADS  MathSciNet  Google Scholar 

  39. Shojai, A., Shojai, F.: Weyl geometry and quantum gravity. Preprint arXiv:gr-qc/0306099 (2003)

  40. Smolin, L.: Towards a theory of spacetime structure at very short distances. Nucl. Phys. B 160, 253–268 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  41. Tann, H.: Einbettung der Quantentheorie eines Skalarfeldes in eine Weyl Geometrie—Weyl Symmetrie und ihre Brechung. Utz, München (1998)

    Google Scholar 

  42. Weyl, H.: Reine Infinitesimalgeometrie. Math. Z. 2, 384–411 (1918). In GA II, 1–28

    Article  MathSciNet  Google Scholar 

  43. Weyl, H.: Raum-Zeit-Materie, 5. Auflage. Springer, Berlin (1923)

    Google Scholar 

  44. Will, C.: The confrontation between general relativity and experiment. Living Reviews in Relativity 4, 1–97 (2001)

    ADS  MathSciNet  Google Scholar 

  45. Zwicky, F.: On the possibilities of a gravitational drag of light. Phys. Rev. 33, 1623f (1929)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department C, Mathematics and Natural Sciences, and Interdisciplinary Center for Science and Technology Studies, University Wuppertal, 42097, Wuppertal, Germany

    Erhard Scholz

Authors
  1. Erhard Scholz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Erhard Scholz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Scholz, E. Cosmological Spacetimes Balanced by a Weyl Geometric Scale Covariant Scalar Field. Found Phys 39, 45–72 (2009). https://doi.org/10.1007/s10701-008-9261-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10701-008-9261-x

Keywords

Search

Navigation