  In this work we investigate the quantum theory of the Kalb-Ramond fields
propagating in $D-$dimensional de Sitter spacetimes using the dynamic invariant
method developed by Lewis and Riesenfeld [J. Math. Phys. 10, 1458 (1969)] to
obtain the solution of the time-dependent Schr\"odinger equation. The wave
function is written in terms of a $c-$number quantity satisfying of the
Milne-Pinney equation, whose solution can be expressed in terms of two
independent solutions of the respective equation of motion. We obtain the exact
solution for the quantum Kalb-Ramond field in the de Sitter background and
discuss its relation with the Cremmer-Scherk-Kalb-Ramond model.
