Implications of a cosmological constant varying as <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">−</mi><mn>2</mn></mrow></msup></mrow></math></span>

Wei Chen; Yong-Shi Wu

doi:10.1103/PhysRevD.41.695

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Implications of a cosmological constant varying as $R^{- 2}$

Wei Chen and Yong-Shi Wu

Department of Physics, University of Utah, Salt Lake City, Utah 84112

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Phys. Rev. D 41, 695 – Published 15 January, 1990Erratum Phys. Rev. D 45, 4728 (1992)

DOI: https://doi.org/10.1103/PhysRevD.41.695

Abstract

We advocate the possibility that the (effective) cosmological constant Λ varies in time as $R^{- 2}$ , R being the scale factor of our expanding Universe. This behavior can be obtained under some simple and general assumptions in conformity with quantum cosmology. After pointing out several advantages worth noticing, we show that such a time-varying Λ leads to no conflict with existing observations. However, it does change the predictions of the standard cosmology in the matter-dominated epoch and alleviates some problems in reconciling observations with the inflationary scenario. In particular, this ‘‘medium’’ time variation of Λ leads to creation of matter with a rate at present which is comparable to that in the steady-state cosmology.

Erratum

Erratum: Implications of a cosmological constant varying as $R^{- 2}$

Wei Chen and Yong-Shi Wu

Phys. Rev. D 45, 4728 (1992)

References (27)

A. Einstein, Sitz. Ber. Preuss, Akad. Wiss. (1917) and (1919) [English translation: The~Principle~of~Relativity (Methuen, 1923, reprinted by Dover, New York, 1924), pp. 177 and 191].
P. A. M. Dirac, Nature (London) 139, 323 (1937).
R. H. Dicke, Nature (London) 192, 440 (1961); see, e.g., S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972).
For recent discussions see, e.g., Y.S. Wu and Z. Wang, Phys. Rev. Lett. 57, 1978 (1986); K. Maeda, Mod. Phys. Lett. A 3, 243 (1988); R. W. Hellings et al., Phys. Rev. Lett. 51, 1609 (1983); T. Damour, G. W. Gibbons and J. H. Taylor, ibid. 61, 1151 (1988).
We use the notations of Weinberg's in Ref. 3. The flat metric has $g_{00}$ = -1.
For a recent comprehensive and critical review of the cosmological-constant problem, see S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).
J. R. Gott, J E. Gunn, D. N. Schramm and B. M. Tinsley, Astrophys. J. 194, 54 (1974).
For an earlier review see, e.g., A. Zee, in High Energy Physics, proceedings of the 20th Annual Orbis Scientiae, edited by S. L. Mintz and A. Perlmutter (Plenum, New York, 1988).
S. W. Hawking, Phys. Lett. 134B, 403 (1984); E. Baum, ibid. 133B, 185 (1983).
S. Coleman, Nucl. Phys. B307, 864 (1988).
S. B. Giddings and A. Strominger, Nucl. Phys. B307, 854 (1988); ibid. B321, 481 (1989).
T. Banks, Nucl. Phys. B309, 493 (1988).
S. Adler, Rev. Mod. Phys. 54, 729 (1982).
L. F. Abbott, Phys. Lett. 150B, 427 (1985); T. Banks, Nucl. Phys. B249, 332 (1985); S. M. Barr, Phys. Rev. D 36, 1691 (1987).
P. J. E. Peebles and B. Ratra, Astrophys. J. Lett. 325, L17 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D 37, 3406 (1988).
K. Freese, F. C. Adams, J. A. Frieman and E. Mottola, Nucl. Phys. B287, 797 (1987).
T. S. Olson and T. F. Jordan, Phys. Rev. D 35, 3258 (1987); M. Ozer and M. O. Taha, Phys. Lett. B 171, 363 (1986); Nucl. Phys. B287, 776 (1987); M. Reuter and C. Wetterich, Phys. Lett. B 188, 38 (1987).
W. A. Hiscock, Phys. Lett. 166B, 285 (1986); L. Ford, Phys. Rev. D 31, 710 (1985).
E. Mottola, Phys. Rev. D 31, 754 (1985); ibid. 33, 1616 (1986); ibid. 33, 2136 (1986); P. Mazur and E. Mottola, Nucl. Phys. B278, 3519 (1986).
A. Strominger, Nucl. Phys. B319, 722 (1989).
A. Guth, Phys. Rev. D 23, 347 (1981).
P. J. E. Peebles, Nature (London) 321, 27 (1986).
E. D. Loh and E. J. Spillar, Astrophys. J. Lett. 307, L1 (1986); E. D. Loh, Phys. Rev. Lett. 57, 2865 (1986).
P. J. E. Peebles, Astrophys. J. 284, 439 (1984); J. E. Gunn and B. M. Tinsley, Nature (London) 257, 454 (1975).
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[c1] A. Einstein, Sitz. Ber. Preuss, Akad. Wiss. (1917) and (1919) [English translation: The~Principle~of~Relativity (Methuen, 1923, reprinted by Dover, New York, 1924), pp. 177 and 191].

[c2] P. A. M. Dirac, Nature (London) 139, 323 (1937).

[c3] R. H. Dicke, Nature (London) 192, 440 (1961); see, e.g., S. Weinberg, Gravitation and Cosmology (Wiley, New York, 1972).

[c4] For recent discussions see, e.g., Y.S. Wu and Z. Wang, Phys. Rev. Lett. 57, 1978 (1986); K. Maeda, Mod. Phys. Lett. A 3, 243 (1988); R. W. Hellings et al., Phys. Rev. Lett. 51, 1609 (1983); T. Damour, G. W. Gibbons and J. H. Taylor, ibid. 61, 1151 (1988).

[c5] We use the notations of Weinberg's in Ref. 3. The flat metric has $g_{00}$ = -1.

[c6] For a recent comprehensive and critical review of the cosmological-constant problem, see S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).

[c7] J. R. Gott, J E. Gunn, D. N. Schramm and B. M. Tinsley, Astrophys. J. 194, 54 (1974).

[c8] For an earlier review see, e.g., A. Zee, in High Energy Physics, proceedings of the 20th Annual Orbis Scientiae, edited by S. L. Mintz and A. Perlmutter (Plenum, New York, 1988).

[c9] S. W. Hawking, Phys. Lett. 134B, 403 (1984); E. Baum, ibid. 133B, 185 (1983).

[c10] S. Coleman, Nucl. Phys. B307, 864 (1988).

[c11] S. B. Giddings and A. Strominger, Nucl. Phys. B307, 854 (1988); ibid. B321, 481 (1989).

[c12] T. Banks, Nucl. Phys. B309, 493 (1988).

[c13] S. Adler, Rev. Mod. Phys. 54, 729 (1982).

[c14] L. F. Abbott, Phys. Lett. 150B, 427 (1985); T. Banks, Nucl. Phys. B249, 332 (1985); S. M. Barr, Phys. Rev. D 36, 1691 (1987).

[c15] P. J. E. Peebles and B. Ratra, Astrophys. J. Lett. 325, L17 (1988); B. Ratra and P. J. E. Peebles, Phys. Rev. D 37, 3406 (1988).

[c16] K. Freese, F. C. Adams, J. A. Frieman and E. Mottola, Nucl. Phys. B287, 797 (1987).

[c17] T. S. Olson and T. F. Jordan, Phys. Rev. D 35, 3258 (1987); M. Ozer and M. O. Taha, Phys. Lett. B 171, 363 (1986); Nucl. Phys. B287, 776 (1987); M. Reuter and C. Wetterich, Phys. Lett. B 188, 38 (1987).

[c18] W. A. Hiscock, Phys. Lett. 166B, 285 (1986); L. Ford, Phys. Rev. D 31, 710 (1985).

[c19] E. Mottola, Phys. Rev. D 31, 754 (1985); ibid. 33, 1616 (1986); ibid. 33, 2136 (1986); P. Mazur and E. Mottola, Nucl. Phys. B278, 3519 (1986).

[c20] A. Strominger, Nucl. Phys. B319, 722 (1989).

[c21] A. Guth, Phys. Rev. D 23, 347 (1981).

[c22] P. J. E. Peebles, Nature (London) 321, 27 (1986).

[c23] E. D. Loh and E. J. Spillar, Astrophys. J. Lett. 307, L1 (1986); E. D. Loh, Phys. Rev. Lett. 57, 2865 (1986).

[c24] P. J. E. Peebles, Astrophys. J. 284, 439 (1984); J. E. Gunn and B. M. Tinsley, Nature (London) 257, 454 (1975).

[c25] J. V. Narlikar, Introduction to Cosmology (Jones and Bartlett, Boston, 1983).

[c26] G. Burbidge and F. Hoyle, Nuovo Cimento 4, 558 (1956).

[c27] W. L. Kraushaar and G. W. Clark, Phys. Rev. Lett. 8, 106 (1962).

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Implications of a cosmological constant varying as $R^{- 2}$

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Erratum: Implications of a cosmological constant varying as R−2

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Implications of a cosmological constant varying as $R^{- 2}$

Erratum: Implications of a cosmological constant varying as $R^{- 2}$