Skip to main content
SpringerLink
Log in

Cosmology as a problem in critical phenomena

  • Conference paper
  • First Online:
Complex Systems and Binary Networks

Part of the book series: Lecture Notes in Physics ((LNP,volume 461-461))

Abstract

Several problems in cosmology and astrophysics are described in which critical phenomena of various types may play a role. These include the organization of the disks of spiral galaxies, various aspects of the problem of structure formation in cosmology, the problem of the selection of initial conditions and parameters in particle physics and cosmology and the problem of recovering the classical limit from non-perturbative formulations of quantum gravity.

A measure of complexity which is suggested by these applications, but which may also have application to other problems, is described.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S. D. M. White, J. F. Navarro, A. E. Evrard, C. S. Frenk, Nature 366 (1993) 429–433

    Article  ADS  Google Scholar 

  2. P. Coles and G. Ellis, The case for an open universe Department of Applied Math prprint, Capetown (1994).

    Google Scholar 

  3. See for example, J. Bachall, in the Proceedings of Some Unsolved Problems in Astrophysics.

    Google Scholar 

  4. Mather, J. C. et al, Ap. J. 354 (1990) L37.

    Article  ADS  Google Scholar 

  5. V. De Lapparent, M.J. Geller and J.P. Huchra Ap. J. 302 (1986) L1; M. P. Haynes and R. Giovanelli, Ap. J. 306 (1986) L55.

    Article  ADS  Google Scholar 

  6. L J For an excellent review, see Garay: “Quantum gravity and minimum length”, Imperial College preprint/TP/93–94/20, gr-qc/9403008 (1994)

    Google Scholar 

  7. F. Hoyle, D. N. F. Dunbar, W. A. Wensel and W. Whaling, Phys. Rev. 92 (1953) 649; F. Hoyl, Galaxies, Nuclei and quasars (Heinemann, London, 1965), p. 146.

    Article  ADS  Google Scholar 

  8. B. J. Carr and M. J. Rees, Nature 278 (1979) 605.

    Article  ADS  Google Scholar 

  9. J. D. Barrow and F. J. Tipler, The Anthropic Cosmological Principle (Oxford University Press, Oxford, 1986).

    Google Scholar 

  10. B. Carter, “The significance of numerical coincidences in nature”, unpublished preprint, Cambridge University, 1967; in Confrontation of Cosmological Theories with Observational Data, IAU Symposium No. 63, ed. M. Longair (Reidel, Dordrecht, 1974) p. 291.

    Google Scholar 

  11. P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. A 38 (1988) 364; Phys. Rev. Lett. 59 (1987) 381.

    Article  ADS  MathSciNet  Google Scholar 

  12. P. Bak and Maya Paczuski, “Complexity, contingency and criticality” Brookhaven preprint.

    Google Scholar 

  13. S. Mineshinge, N. B. Ouchi and H. Nishimori, PASJ 46 (1994) 97; S. Mineshinge, M. Takeuchi and H. Nishimori, Ap. J. 435 (1994) L125.

    ADS  Google Scholar 

  14. H. Gerola and P. E. Seiden, Ap. J. 223 (1978) 129; P. E. Seiden, L. S. Schulman and H. Gerola, Stochastic star formation and the evolution of galaxies, Astrophys. J. 232 (1979) 702–706; P. E. Seiden and L. S. Schulman, Percolation and galaxies Science 233 (1986) 425–431 Percolation model of galactic structure, Advances in Physics, 39 (1990) 1–54; L. S. Schulman, “Modeling galaxies: cellular automana and percolation”, to appear in Cellular Automata: Prospects in Astrophysical Applications, A. Lejeune and J. Perdang, eds. World Scientific, Singapore (1993).

    Article  ADS  Google Scholar 

  15. P. Seiden, L.S. Schulman and H. Gerola, Ap. J. 232 (1979) 702.

    Article  ADS  Google Scholar 

  16. See, for example: J. Franco and D. P. Cox, Self-regulated star formation in the galaxy, Astrophys. J. 273 (1983) 243–248; J. Franco and S. N. Shore The galaxy as a self-regulated star forming system: The case of the OB associations Astrophys. J. 285 (1984) 813–817; S. Ikeuchi, A. Habe and Y. D. Tanaka The interstellar medium regulated by supernova remnants and bursts of star formation MNRAS 207 (1984) 909–927; R.F.G. Wyse and J. Silk Evidence for supernova regulation of metal inrichment in disk galaxies Astrophys. J. 296 (1985) 11–15; M. A. Dopita, A law of star formation in disk galaxies: Evidence for self-regulating feedback Astrophys. J. 295 (1985) L5–L8; G. Hensler and A. Burkert, Self-regulated star formation and evolution of the interstellar medium Astrophys. and Space Sciences 171 (1990) 149–156.

    Article  ADS  Google Scholar 

  17. R. F. G. Wyse and J. Silk, Astrophys. J. 339 (1989) 700.

    Article  ADS  Google Scholar 

  18. See, for example, The Physics and Chemistry of Interstellar Molecular Clouds ed. G. Winnewisser and J.T. Armstrong, Springer Verlag Lecture Notes in Physics 331 (1989); Molecular Coulds in the Milky Way and External Galaxies ed. R. L. Dickman, R. L. Snell and J. S. Young Springer Verlag Lecture Notes in Physics 315 (1988).

    Google Scholar 

  19. B. G. Elmegreen Triggered Star Formation IBM Research Report, in the Proceedigs of the III Canary Islands Winter School, 1991, eds. G. Tenorio-Tagle, M. Prieto and F. Sanchez (Cambridge University Press, Cambridge, 1992).

    Google Scholar 

  20. B. G. Elmegreen, Large Scale Dynamics of the Interstellar Medium, to appear in Interstellar Medium, processes in the galactic diffuse matter ed. D. Pfenniger and P. Bartholdi, Springer Verlag, 1992.

    Google Scholar 

  21. A. Parravano, Self-regulating star formation in isolated galaxies: thermal instabilities in the interstellar medium Astron. Astrophys. 205 (1988) 71–76; A selfregulated star formation rate as a function of global galactic parameters Astrophys. J. 347 (1989) 812–816; A. Parravano and J. Mantilla Ch., A self-regulated state for the interstellar medium: radial dependence in the galactic plane, Atrophys. J. 250 (1991) 70–83; A. Parravano, P. Rosenzweig and M. Teran, Galactic evolution with self-regulated star formation: stability of a simple one-zone model Astrophys. J. 356 (1990) 100–109.

    ADS  Google Scholar 

  22. See, for example, F. H. Shu, F. C. Adams and S. Lizano Star formation in molecular clouds: observation and theory in Ann. Rev. Astron. Astrophy., 25 (1987) 23–81 and C. J. Lada and F. H. Shu, The formation of sunlike stars Berkely preprint, to appear in Science and references contained therein.

    Google Scholar 

  23. E. E. Salpeter, Astrophys. J. 121 (1955) 161.

    Article  ADS  Google Scholar 

  24. G. E. Miller and J. Scalo, Ap. J. Suppl. 41 (1979) 513; J. Scalo, Fundamentals of Cosmic Physics 11 (1986) 1–278.

    Article  ADS  Google Scholar 

  25. R. B. Larson M.N.R.A.S. 214 (1985) 379; 218 (1986) 409.

    ADS  Google Scholar 

  26. J. Scalo, in Physical Processes in Fragmentation and Star Formation ed. R. Capuzzo-Dolcetta, C. Ciosi and A. Di Fazio (Klower, 1990)

    Google Scholar 

  27. B. Elmegreen and M. Thomasson, Grand design and flocculent spiral structure in computer simulations with star formation and gas heating Astron. and Astrophys. (1992)?.

    Google Scholar 

  28. M. Bucher, A. S. Goldhaber and N. Turok, “An open universe from inflation”, hep-ph/9411206, iassns-hep-94-81. PUPT-94-1507; M. Bucher and N. Turok, “Open inflation with arbitrary false vacuum mass” hep-ph 9503393, PUPT-95-1518; J.R. Gott, Nature 295 (1982) 304.

    Google Scholar 

  29. Walker, T. P, Steigman, G., Kang, H.-S., Schramm, D. M., & Olive, K. 1991

    Google Scholar 

  30. See, for example, S. D. M. White, MAP preprint, 1994; S. D. M. White and C. S. Frenk, Ap. J. (1991) 379, 52; G. Efstathios and J. Silk, Fund. Cos. Phys. 9 (1983) 1.

    Google Scholar 

  31. J.P. Ostriker and L.L. Cowie, Ap. J. 243 (1981) L127.

    Article  ADS  Google Scholar 

  32. S. Ikeuchi, Publ. Astron. Soc. Japan 33 (1981) 211.

    ADS  Google Scholar 

  33. J.P. Ostriker, C. Thompson and E. Witten, Phys. Lett. B (1986).

    Google Scholar 

  34. R.A. Daley (1986)

    Google Scholar 

  35. N. Yu. Gnedin and J. P. Ostriker, Astrophys. J. 400 (1992) 1–20

    Article  ADS  Google Scholar 

  36. P.J.E. Peebles, in The Early Universe ed. W.G. Unruh and G.W. Semenoff, D. Reidal Publishing, 1988, p. 203; in the proceedings of the 8th IAP meeting, First light in the universe

    Google Scholar 

  37. C. Hogan, Ap. J. 415 (1993) L63–66.

    Article  ADS  Google Scholar 

  38. P. Petitjean, J. K. Webb, M. Rauch, R.F. Carswell and K. Lanzetta, MNRAS 262 (1993) 499; K.M. Lanzetta, A. M. Wolfe, D. Ai Turnshek, Limin Lu, R.G. McMahon and C. Hazard, Ap. J. Suppl. Series. 77 (1991) 1.

    ADS  Google Scholar 

  39. J. Charlton, E. Salpeter and C. J. Hogan, Ap. J. 402 (1993) 493; J. Charlton, E. Salpeter and S. M. Linder, “Competition between pressure and gravity confinement in Lyman alpha forest observations”, ApJ, 430, L29 (1994).

    Article  ADS  Google Scholar 

  40. Lanzetta, K. M., Bowen, D. V., Tytler, D., and Webb, J. K. 1995, ApJ, 442, 538; Steidel, C. 1995, in Proceedings of ESO Workshop on QSO Absorption Lines, ed. G. Meylan, (Springer-Verlag: heidelberg), in press

    Article  ADS  Google Scholar 

  41. Richard Ellis “The morphological evolution of galaxies” in Unsolved Problems in Astrophysics op. cit.

    Google Scholar 

  42. Broadhurst, R. J., Ellis, R. S., & Shanks, T. 1988, MNRAS, 235, 927 Colless, M. M., Ellis, R. S., Taylor, K., & Hook, R. N. 1989, MNRAS, 244,408 Songaila, A., Cowie, L. L., Hu, E. M., & Gardner, J. P. 1994, ApJS, 44, 461

    Google Scholar 

  43. J. Peebles, Principles of Physical Cosmology (Princeton University Press, 1993).

    Google Scholar 

  44. For a general review, see N. Bachall and J. Ostriker, in the Proceedings of the Conference on Unsolved problems in Astrophysics, op. cit.. See also R.Y. Cen and J. P. Ostriker, Ap. J. 339 (1992) L113; 404 (1993) 415; 417 (1993) 415; D. Ryu, J.P. Ostriker, H. Kang and R.Y. Cen, Ap.J. 414 (1993) 1

    Google Scholar 

  45. M. Carfora and K. Piotrokowska, “A renormalization group approach to relativistic cosmology”, to appear in Phys. Rev. D.

    Google Scholar 

  46. W. H. Press and P. Schecter, Ap. J. 187 (1974) 425.

    Article  ADS  Google Scholar 

  47. S. D. M. White, G. Efstathiou and C. S. Frenk, Mon. Not. R. Astro. Soc. 262 (1993) 1023; A. Klypin, J. Holtzmann, J. Primack and E. Regos Ap. J. 416 (1993) 1; Lacey and Cole, MNRAS (1994)

    ADS  Google Scholar 

  48. K. Chen and P. Bak, Phys. Lett. A 140 (1989) 299.

    Article  ADS  Google Scholar 

  49. L. S. Schulman and P. E. Seiden, Ap. J. 311 (1986) 1.

    Article  ADS  Google Scholar 

  50. B.J. Carr, “Baryonic dark matter”, to appear in AnnualReviews of Astronomy and Astrophysics, 1995.

    Google Scholar 

  51. A. Strominger, “Massless black holes and conifolds in string theory”, preprint hep-th/9504090.

    Google Scholar 

  52. L. Smolin Classical and Quantum Gravity 9 (1992) 173–191

    Article  ADS  MathSciNet  Google Scholar 

  53. L. Smolin, On the fate of black hole singularities and the parameters of the standard model gr-gc??

    Google Scholar 

  54. L. Smolin, The Life of the Cosmos to appear in Oct. 95, Crown Press, New York, and Orion Press, London.

    Google Scholar 

  55. J.A. Wheeler, in Gravitation, by C. Misner, K. Thorne and J. A. Wheeler, last chapter.

    Google Scholar 

  56. E. Martinec, 1994, hep-th/9412074

    Google Scholar 

  57. R. Gott, private communication.

    Google Scholar 

  58. G. E. Brown and H. A. Bethe, Astro. J. 423 (1994) 659; 436 (1994) 843, G. E. Brown, Nucl. Phys. A574 (1994) 217; G. E. Brown, “Kaon condensation in dense matter”; H. A. Bethe and Ge. E. Brown, “Observational constraints on the maximum neutron star mass”, preprints.

    Article  ADS  Google Scholar 

  59. S. E. Thorsett, Z. Arzoumanian, M.M. McKinnon and J. H. Taylor Astrophys. Journal Letters 405 (1993) L29

    Article  Google Scholar 

  60. M. Rees, MNRAS 176 (1976) 483; J. Silk Ap. J. 211 (1976) 638.

    ADS  Google Scholar 

  61. For a review, see J. Ambjorn, J. Jerkiewicz and Y. Watabiki, “Dynamical triangutations, a gateway to quantum gravity”, NBI-HE-95-08, to appear in J. Math. Phys. Nov. 1995.

    Google Scholar 

  62. M.E. Agishtein and A.A. Migdal, Nucl. Phys. B 385 (1982) 395.

    Article  ADS  MathSciNet  Google Scholar 

  63. J. Ambjorn, J. Jerkiewicz and C. F. Kristjansen, Nucl. Phys. B 393 (1993) 601; Phys. Lett. B305 (1993) 208; J. Ambjorn, Z. Burda, J. Jerkiewicz and C. F. Kristjansen, Phys. Rev. d48 (1993) 3695.

    Article  ADS  Google Scholar 

  64. H. W. Hamber, Nucl Phys. B (Proc. Supp.) 20 (1991) 728; 25A (1992) 150; B400 (1993) 347; Phys. Rev. D45 (1992) 507; H. W. Hamber and R. M. williams, Nucl. Phys. B415 (1994) 463.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  65. T. Regge, Nuovo Cimento 19 (1961) 558.

    Article  MathSciNet  Google Scholar 

  66. S. Weinberg, in General relativity: An Einstein Survey ed. S. Hawking and W. Israel (Cambridge University Press, 1979). L. Smolin, Nuclear Physics B208 (1982) 439.

    Google Scholar 

  67. C Rovelli: Class Quant Grav 8 (1991) 1613

    Article  MATH  ADS  MathSciNet  Google Scholar 

  68. A Ashtekar: Non perturbative canonical gravity, World scientific, Singapore 1991

    MATH  Google Scholar 

  69. L Smolin: in Quantum Gravity and Cosmology, eds J Pérez-Mercader et al, World Scientific, Singapore 1992

    Google Scholar 

  70. A Ashtekar C Rovelli L Smolin: Phys Rev Lett 69 (1992) 237

    Article  MATH  ADS  MathSciNet  Google Scholar 

  71. C. Rovelli and L. Smolin, Discreteness of volume and area in quantum gravity, to appear in Nucl. Phys. B 1995.

    Google Scholar 

  72. R Penrose: in Quantum theory and beyond ed T Bastin, Cambridge U Press 1971; in Advances in Twistor Theory, ed. L. P. Hughston and R. S. Ward, (Pitman, 1979) p. 301; in Combinatorial Mathematics and its Application (ed. D. J. A. Welsh) (Academic Press, 1971).

    Google Scholar 

  73. C. Rovelli and L. Smolin, “Spin networks and quantum gravity” Penn State CGPG-95/4-4 and IASSNS-HEP-95/27 preprint, gr-qc/9505006.

    Google Scholar 

  74. L Smolin: in Directions in General Relativity, v. 2, papers in honour of Dieter Brill, ed BL Hu T Jacobson, Cambridge University Press, Cambridge 1994

    Google Scholar 

  75. C. Rovelli and L. Smolin, Phys Rev Lett 72 (1994) 446

    Article  MATH  ADS  MathSciNet  Google Scholar 

  76. R. Borissov, C. Rovelli and L. Smolin, Nonperturbative dynamics of quantum general relativity preprint in preparation. C. Rovelli, to appear in J. Math Phys. Nov. (1995).

    Google Scholar 

  77. J Iwasaki C Rovelli: Int J of Mod Phys D 1 (1993) 533; Class and Quantum Grav 11 (1994) 1653

    Article  ADS  MathSciNet  Google Scholar 

  78. J. Stachel, Einstein's search for general covariance 1912–1915 in Einstein and the History of General Relavity ed. by D. Howard and J. Stachel, Einstein Studies, Volume 1 (Birkhauser, Boston, 1989).

    Google Scholar 

  79. Leibniz, The Monadology in Leibniz, Philosophical Writings ed. G.H.R. Parkinson, translated by M. Morris and G.H.R. Parkinson (Dent, London, 1973)

    Google Scholar 

  80. J. B. Barbour and L. Smolin, Syracuse University preprint, SU-GP-92/2–4, see also J. B. Barbour, “On the origin of structure in the universe,” presented at the “3d Philosophy and Physics Workshop”, Forschungsstatte der Evangelischen Studiengemeinschaft (FEST) in Heidelberg, May 1990. To be published in “Philosophy and Modern Physics”, publ. by Springer; Mathematical Modeling of the Monodology, submitted for publication and L. Smolin Space and Time in the Quantum Universe in Conceptual Problems of Quantum Gravity ed. by A. Ashtekar and J. Stachel, (Birkhauser, Boston, 1991).

    Google Scholar 

Download references

Author information

Author notes

  1. Lee Smolin

    Present address: School of Natural Sciences, Institute for Advanced Study, 08540, Princeton, New Jersey, USA

Authors and Affiliations

  1. Center for Gravitational Physics and Geometry, Department of Physics, Pennsylvania State University, 16802-6360, University Park, Pa, USA

    Lee Smolin

Authors
  1. Lee Smolin
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Lee Smolin .

Editor information

Ramón López-Peña Henri Waelbroeck Riccardo Capovilla Ricardo García-Pelayo Federico Zertuche

Rights and permissions

Reprints and permissions

Copyright information

© 1995 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Smolin, L. (1995). Cosmology as a problem in critical phenomena. In: López-Peña, R., Waelbroeck, H., Capovilla, R., García-Pelayo, R., Zertuche, F. (eds) Complex Systems and Binary Networks. Lecture Notes in Physics, vol 461-461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103573

Download citation

  • DOI: https://doi.org/10.1007/BFb0103573

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60339-9

  • Online ISBN: 978-3-540-44937-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation