  Two different ways of generalizing Einstein's general theory of relativity
with a cosmological constant to Brans-Dicke type scalar-tensor theories are
investigated in the linearized field approximation. In the first case a
cosmological constant term is coupled to a scalar field linearly whereas in the
second case an arbitrary potential plays the role of a variable cosmological
term. We see that the former configuration leads to a massless scalar field
whereas the latter leads to a massive scalar field. General solutions of these
linearized field equations for both cases are obtained corresponding to a
static point mass. Geodesics of these solutions are also presented and solar
system effects such as the advance of the perihelion, deflection of light rays
and gravitational redshift were discussed. In general relativity cosmological
constant has no role on these phenomena. We see that for the Brans-Dicke theory
the cosmological constant has also no effect on these phenomena. This is
because solar system observations require very large values of the Brans-Dicke
parameter and the correction terms to these phenomena becomes identical to GR
for these large values of this parameter. This result is also observed for the
theory with arbitrary potential if the mass of the scalar field is very light.
For a very heavy scalar field, however, there is no such limit on the value of
this parameter and there are ranges of this parameter where these contributions
may become relevant in these scales. Galactic and intergalactic dynamics is
also discussed for these theories at the latter part of the paper with similar
conclusions.
