  In this paper we study how to include the cosmological constant in geometric
scalar theory of gravity (GSG). Firstly we show that the cosmological constant
could not be modeled by a matter field, unlike in General Relativity. We also
show that a spherically symmetric matter distribution, over the de Sitter
vacuum, does not produce the Kottler solution and no black hole. To circumvent
this problem we introduce an coupling term between the scalar field and the
vacuum curvature in way to provide the Kottler solution. We also apply the
original (GSGI) and the modified (GSGII) geometric scalar theory of gravity to
the Friedmann-Robertson-Walker cosmology. A numerical analysis indicates that
GSGII is most sensible to the cosmological constant them GSGI.
