Abstract
A way to reconcile Dirac's large numbers hypothesis and Einstein's theory of gravitation wasrecently suggested by Lau (1985). It is characterized by the conjecture of a time-dependentcosmological term and gravitational term in Einstein's field equations. Motivated by thisconjecture and the large numbers hypothesis, we formulate here a scalar-tensor theory in terms of an action principle. The cosmological term is required to be spatially dependent as well as time dependent in general. The theory developed is applied to a cosmological model compatible with the large numbers' hypothesis. The time-dependent form of the cosmological term and the scalar potential are then deduced. A possible explanation of the smallness of the cosmological term is also given and the possible significance of the scalar field is speculated.
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