Skip to main content

How Heavy Is the Vacuum?

  • Chapter
  • First Online:
  • 1433 Accesses

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

Abstract

Well into the 1990s, most cosmologists preferred not to speak of the cosmological constant. This attitude was justified partly by the deep theoretical uncertainty surrounding the status of vacuum energy, and partly by the degree of fine-tuning that seemed to be implied in models whose density of vacuum energy was comparable to that of matter. Nevertheless the cosmological constant was trotted out whenever some crisis arose within cosmology that could not be explained any other way. Two examples that received attention in the 1960s were the concentration of quasars within a narrow range of high redshifts, and the tension between the age of the universe implied by measurements of the Hubble expansion rate and the age of the oldest stars. In the 1980s, vacuum energy was revived again to bridge the gap between the observed low density of matter and the expectation (based on inflation) that the total density of the universe should be exactly critical. The lack of anisotropy observed in the cosmic microwave background prior to 1992 was also taken as possible evidence for a \(\varLambda \) term. Tentative measurements of a nonzero dark-energy density were first obtained with counts of faint galaxies and analyses of absorption lines in the Lyman-\(\alpha \) forest, but seemed to conflict with upper limits based on the statistics of gravitational lenses.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    This problem goes back to 1930 with Hubble’s original and erroneously high value for the expansion rate (Kragh 1996, pp. 73–79 and references therein).

  2. 2.

    Fukugita later recalled that invoking the cosmological constant was treated by many at the time as a “crime, or offense against the rules” (Fukugita 2014).

References

  • Chae, K.-H., et al.: Constraints on cosmological parameters from the analysis of the Cosmic Lens All-Sky Survey radio-selected ravitational lens statistics. Phys. Rev. Lett. 89, 151301, 4 (2002)

    Google Scholar 

  • Chiba, M., Yoshii, Y.: New limits on a cosmological constant from statistics of gravitational lensing. Astrophys. J. 510, 42–53 (1999)

    Article  ADS  Google Scholar 

  • Dicke, R.H.: Gravitation and the Universe. American Philosophical Society, Philadelphia (1970)

    Google Scholar 

  • Durrer, R., Straumann, N.: The cosmological constant and galaxy formation. Mon. Not. R. Astron. Soc. 242, 221–223 (1990)

    ADS  Google Scholar 

  • Eddington, A.S.: The Mathematical Theory of Relativity, p. 154. Cambridge University Press, Cambridge (1924)

    Google Scholar 

  • Efstathiou, G., Sutherland, W.J., Maddox, S.J.: The cosmological constant and cold dark matter. Nature 348, 705–707 (1990)

    Article  ADS  Google Scholar 

  • Falco, E.E., Kochanek, C.S., Muñoz, J.A.: Limits on cosmological models from radio-selected gravitational lenses. Astrophys. J. 494, 47–59 (1998)

    Article  ADS  Google Scholar 

  • Feldman, H.A., Evrard, A.E.: Structure in a loitering universe. Int. J. Mod. Phys. D2, 113–122 (1993)

    Article  ADS  Google Scholar 

  • Fukugita, M., Yamashita, K., Takahara, F., Yoshii, Y.: Test for the cosmological constant with the number count of faint galaxies. Astrophys. J. 361, L1–L4 (1990a)

    Google Scholar 

  • Fukugita, M., Futamase, T., Kasai, M.: A possible test for the cosmological constant with gravitational lenses. Mon. Not. R. Astron. Soc. 246, 24P–27P (1990b)

    Google Scholar 

  • Fukugita, M.: Personal communication. Email, Feb. 7, 2014 (2014)

    Google Scholar 

  • Gardner, J.P., Cowie, L.L., Wainscoat, R.J.: Galaxy number counts from \(K=10\) to \(K=23\). Astrophys. J. 415, L9–L12 (1993)

    Article  ADS  Google Scholar 

  • Hoell, J., Priester, W.: Void-structure in the early universe. Implications for a \(\Lambda > 0\) cosmology. Astron. Astrophys. 251, L23–L26 (1991)

    ADS  Google Scholar 

  • Hoell, J., Liebscher, D.-E., Priester, W.: Confirmation of the Friedmann-Lemaître universe by the distribution of the larger absorbing clouds. Astron. Nachr. 315, 89–96 (1994)

    Article  ADS  MATH  Google Scholar 

  • Keeton, C.R.: Rethinking lensing and \(\Lambda \). Astrophys. J. 575, L1–L4 (2002)

    Article  ADS  Google Scholar 

  • Kochanek, C.S.: Is there a cosmological constant? Astrophys. J. 466, 638 (1996)

    Article  ADS  Google Scholar 

  • Kragh, H.: Cosmology and Controversy, pp. 52–53. Princeton University Press, Princeton (1996)

    Google Scholar 

  • Krauss, L.M., Turner, M.S.: The cosmological constant is back. Gen. Relativ. Gravit. 27, 1137–1144 (1995)

    Article  ADS  MATH  Google Scholar 

  • Lahav, O., Lilje, P.B., Primack, J.R., Rees, M.J.: Dynamical effects of the cosmological constant. Mon. Not. R. Astron. Soc. 251, 128–136 (1991)

    ADS  Google Scholar 

  • Liebscher, D.-E., Priester, W.: A new method to test the model of the universe. Astron. Astrophys. 261, 377–381 (1992)

    ADS  Google Scholar 

  • Loh, E.D.: Implications of the red-shift-number test for cosmology. Phys. Rev. Lett. 57, 2865–2867 (1986)

    Article  ADS  Google Scholar 

  • Malhotra, S., Rhoads, J.E., Turner, E.L.: Through a lens darkly: evidence for dusty gravitational lenses. Mon. Not. R. Astron. Soc. 368, 138–144 (1997)

    Article  ADS  Google Scholar 

  • Maoz, D.: Quasar lensing statistics and \(\Omega _{\Lambda }\): what went wrong? Proc. Int. Astron. Union 2004, 413–418 (2004)

    Article  Google Scholar 

  • Martel, H., Wasserman, I.: Simulation of cosmological voids in \({\Lambda } > 0\) Friedmann models. Astrophys. J. 348, 1–25 (1990)

    Article  ADS  Google Scholar 

  • Martel, H.: Galaxy formation in \({\Lambda } > 0\) Friedmann models: consequences for the number counts versus redshift test. Astrophys. J. 421, L67–L70 (1994)

    Google Scholar 

  • Ostriker, J.P., Steinhardt, P.J.: The observational case for a low-density universe with a non-zero cosmological constant. Nature 377, 600–602 (1995). This paper was originally titled “Cosmic concordance” when it appeared in preprint form as arXiv:astro-ph/9505066

  • Overduin, J., Priester, W.: Quasar absorption-line number density in a closed, \(\Lambda \)-dominated universe. Astrophys. Space Sci. 305, 159–163 (2006)

    Google Scholar 

  • Overduin, J., Blome, H.-J., Hoell, J.: Wolfgang Priester: from the big bounce to the \(\Lambda \)-dominated universe. Naturwissenschaften 94, 417–429 (2007)

    Article  ADS  Google Scholar 

  • Peebles, P.J.E.: Tests of cosmological models constrained by inflation. Astrophys. J. 284, 439–444 (1984)

    Article  ADS  Google Scholar 

  • Peebles, P.J.E.: Principles of Physical Cosmology. Princeton University Press, Princeton (1993)

    Google Scholar 

  • Perlmutter, S., et al.: Measurements of the cosmological parameters \(\Omega \) and \(\Lambda \) from the first seven supernovae at \(z\ge 0.35\). Astrophys. J. 483, 565–581 (1997)

    Article  ADS  Google Scholar 

  • Priester, W.: The scale of the universe: a unit of length. Comments Astrophys. 17, 327–342 (1995)

    ADS  Google Scholar 

  • Rindler, W.: Essential Relativity: Special, General and Cosmological. Van Nostrand Reinhold, New York (1969)

    Book  MATH  Google Scholar 

  • Sahni, V., Feldman, H., Stebbins, A.: Loitering universe. Astrophys. J. 385, 1–8 (1992)

    Article  ADS  Google Scholar 

  • Sandage, A.: The ability of the 200-inch telescope to discriminate between selected world models. Astrophys. J. 133, 355–392 (1961)

    Article  ADS  MathSciNet  Google Scholar 

  • Totani, T., Yoshii, Y., Sato, K.: Evolution of the luminosity density in the universe: implications for the nonzero cosmological constant. Astrophys. J. 483, L75–L78 (1997)

    Article  ADS  Google Scholar 

  • Totani, T., Yoshii, Y.: Unavoidable selection effects in the analysis of faint galaxies in the Hubble Deep Field: probing the cosmology and merger history of galaxies. Astrophys. J. 540, 81–98 (2000)

    Article  ADS  Google Scholar 

  • Turner, E.L.: Gravitational lensing limits on the cosmological constant in a flat universe. Astrophys. J. 365, L43–L46 (1990)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Helge S. Kragh .

Rights and permissions

Reprints and permissions

Copyright information

© 2014 The Author(s)

About this chapter

Cite this chapter

Kragh, H.S., Overduin, J.M. (2014). How Heavy Is the Vacuum?. In: The Weight of the Vacuum. SpringerBriefs in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55090-4_11

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-55090-4_11

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-55089-8

  • Online ISBN: 978-3-642-55090-4

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics