  We consider bosonic open string field theory in marginally deformed
backgrounds, which is obtained by expanding the string field around the
identity-based solutions associated with marginal deformations. We find a new
set of string fields which satisfies the KBc algebra, but the nilpotent kinetic
operator is that of the theory expanded around the identity-based marginal
solution. By use of these string fields, we construct the tachyon vaccum
solution in marginally deformed backgrounds. The vacuum energy density is
equivalent to that of the tachyon vacuum without marginal deformations. The
gauge invariant overlap is changed according to the effect of marginal
deformations, as expected from known results in CFT. These results suggest that
the vacuum energy is zero for the identity-based marginal solutions in the
original theory.
