FLAT FRW MODELS WITH VARIABLE-G AND VARIABLE-LAMBDA

We consider Einstein's equations with variable gravitational coupling G and cosmological term-LAMBDA. For a power-law time-dependence of G, the cosmological term varies in proportion to the inverse square of the time, provided the equation of state is not that of vacuum. There is then no dimensional constant associated with LAMBDA. For a vacuum equation of state the model is compatible with classical inflation for a wide class of functions G(t) and LAMBDA(t). For non-power-law behaviour of G(t), it is possible to have a scale factor that increases exponentially without a vacuum equation of state. For this case the energy density associated with LAMBDA decreases exponentially, while at time zero it is equal with opposite sign to the regular energy density, so there is zero total energy initially.