## 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/G_{0} = HH_{0}^{-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 β_{a} as functions of R_{E}, where R and R_{E} 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 q̅_{0}, the deceleration parameter in gravitational units, and β̇s_{a}(t_{0})H_{0}^{-1} where β̇s_{a}(t_{0}) is the present epoch value of the derivative of β_{a} with respect to atomic time. We find that a necessary condition for the LNH to be compatible with a Robertson-Walker model is that β̇s_{a}(t_{0})H_{0}^{-1} ≥ 1/2. The only experimental values for β̇s_{a}(t_{0}) available at present are those based on the lengthening of the Moon's period of revolution around the Earth, suggesting 0.86 ≥ β̇s_{a}(t_{0})H_{0}^{-1} ≥ 0.21; the more promising technique of radar ranging to the inner planets has not yet produced a value for β̇s_{a}(t_{0}). Using the lunar data, it follows that 0 ≤ q̅_{0} ≲ 0.42 corresponding to an open universe (k=-1). Closed models (k=1,q̅_{0}>1/2) are not compatible with the LNH since the required values of β̇s_{a}(t_{0})H_{0}^{-1} are more than an order of magnitude above the observational upper limit.

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- Presented at the Dirac Symposium, Loyola University, New Orleans, 1981.

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#### BibTeX Citation

@article{go01500p, author={Goldman, I.}, title={Large number hypothesis and the matter-dominated universe}, year={1982}, journal={International Journal of Theoretical Physics}, volume={21}, pages={665--672}, doi={10.1007/BF02650232}, }

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#### RIS Citation

TY - CPAPER 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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