Publication Abstracts

Goldman 1982

Goldman, I., 1982: Large number hypothesis and the matter-dominated universe. Int. J. Theor. Phys., 21, 665-672, doi:10.1007/BF02650232.

Dirac's large number hypothesis (LNH), in the form G/G0 = HH0-1, is applied to the matter-dominated cosmological era, using the framework of the scale covariant theory (Canuto et al., 1977). We obtain explicit expressions for R and βa as functions of RE, where R and RE are the scale factors of the cosmological Robertson-Walker metric, expressed in atomic and gravitational units, respectively, and β a is the ratio between the rates of gravitational and atomic clocks. The parameters in these expressions are q̅0, the deceleration parameter in gravitational units, and β̇sa(t0)H0-1 where β̇sa(t0) is the present epoch value of the derivative of βa with respect to atomic time. We find that a necessary condition for the LNH to be compatible with a Robertson-Walker model is that β̇sa(t0)H0-1 ≥ 1/2. The only experimental values for β̇sa(t0) available at present are those based on the lengthening of the Moon's period of revolution around the Earth, suggesting 0.86 ≥ β̇sa(t0)H0-1 ≥ 0.21; the more promising technique of radar ranging to the inner planets has not yet produced a value for β̇sa(t0). Using the lunar data, it follows that 0 ≤ q̅0 ≲ 0.42 corresponding to an open universe (k=-1). Closed models (k=1,q̅0>1/2) are not compatible with the LNH since the required values of β̇sa(t0)H0-1 are more than an order of magnitude above the observational upper limit.

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BibTeX Citation

  author={Goldman, I.},
  title={Large number hypothesis and the matter-dominated universe},
  journal={International Journal of Theoretical Physics},

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RIS Citation

ID  - go01500p
AU  - Goldman, I.
PY  - 1982
TI  - Large number hypothesis and the matter-dominated universe
JA  - Int. J. Theor. Phys.
JO  - International Journal of Theoretical Physics
VL  - 21
SP  - 665
EP  - 672
DO  - 10.1007/BF02650232
ER  -

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