  Weak field gravitational wave solutions are investigated in Brans-Dicke (BD)
theory in the presence of a cosmological constant. In this setting the
background geometry is not flat but asymptotically de-Sitter. We investigate
the linearised field equations, and their gravitational wave solutions in a
certain gauge choice. We will show that this theory leads to massless scalar
waves as in original BD theory and in contrast to massive BD theory. The
effects of these waves on free particles and their polarization properties are
studied extensively and effects of the cosmological constant is analyzed in
these phenomena in detail. The energy flux of these waves are also discussed in
this background. By analyzing this flux, we obtain a critical distance where
the waves cannot propagate further, which extends Cosmic no Hair Conjecture
(CNC) to BD theory with a cosmological constant.
