  We study a gravitational model in which scale transformations play the key
role in obtaining dynamical $G$ and $\Lambda$. We take a scale non-invariant
gravitational action with a cosmological constant and a gravitational coupling
constant. Then, by a scale transformation, through a dilaton field, we obtain a
new action containing cosmological and gravitational coupling terms which are
dynamically dependent on the dilaton field with Higgs type potential. The
vacuum expectation value of this dilaton field, through spontaneous symmetry
breaking on the basis of anthropic principle, determines the time variations of
$G$ and $\Lambda$. The relevance of these time variations to the current
acceleration of the universe, coincidence problem, Mach's cosmological
coincidence and those problems of standard cosmology addressed by inflationary
models, are discussed. The current acceleration of the universe is shown to be
a result of phase transition from radiation toward matter dominated eras. No
real coincidence problem between matter and vacuum energy densities exists in
this model and this apparent coincidence together with Mach's cosmological
coincidence are shown to be simple consequences of a new kind of scale factor
dependence of the energy momentum density as $\rho \sim a^{-4}$. This model
also provides the possibility for a super fast expansion of the scale factor at
very early universe by introducing exotic type matter like cosmic strings.
