  In this paper we investigate the vacuum polarization effect associated with a
quantum massive scalar field in a higher dimensional de Sitter spacetime in the
presence of a cosmic string. Because this investigation has been developed in a
pure de Sitter space, here we are mainly interested on the effects induced by
the presence of the string. So this analysis is developed by expressing the
complete Wightman function as the sum of two terms: The first one corresponds
to the bulk where the cosmic string is absent and the second one is induced by
the presence of the string. By using the Abel-Plana summation formula, we show
that for points away from the string the latter is finite at the coincidence
limit and it is used to evaluate the vacuum averages of the square of the field
and the energy-momentum tensor induced by the cosmic string. Simple asymptotic
formulae are obtained for these expectation values for points near the string
and at large distances from it. It is shown that, depending on the curvature
radius of de Sitter spacetime, two regimes are realized with monotonic and
oscillatory behavior of the vacuum expectation values at large distances.
