  There exists a growing body of observational evidence supporting a
non-vanishing cosmological constant at the present epoch. We examine the
possibility that such a term may arise directly from the potential energy which
drove an inflationary expansion of the very early universe. To avoid arbitrary
alterations in the shape of this potential at various epochs it is necessary to
introduce a time-dependent viscosity into the system. The evolution of the
effective Planck mass in scalar-tensor theories is a natural candidate for such
an effect. In these models there are observational constraints arising from
anisotropies in the cosmic microwave background, large-scale galactic
structure, observations of the primordial Helium abundance and solar system
tests of general relativity. Decaying power law and exponential potentials are
considered, but for these models it is very difficult to simultaneously satisfy
all of the limits. This may have implications for the joint evolution of the
gravitational and cosmological constants.
