Abstract
In the Brans-Dicke theory, a certain large number hypothesis is equivalent implicitly to an equation of state. The equation of state corresponding to Dirac's large number hypothesis, however, is not reasonable. The Whitrow-Randall relation is regarded as a modification of Dirac's large number hypothesis, but it is not in fact in keeping with Dirac's original intention to relate only a single cosmological parameter to the gravitational “constant.” In view of those facts, an alternative modification of Dirac's large number hypothesis is proposed.
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