  Given a complete Riemannian manifold $M$ with a lower Ricci curvature bound,
we consider barycenters in the Wasserstein space $\mathcal{W}_2(M)$ of
probability measures on $M$. We refer to them as Wasserstein barycenters, which
by definition are probability measures on $M$. The goal of this article is to
present a novel approach to proving their absolute continuity. We introduce a
new class of displacement functionals exploiting the Hessian equality for
Wasserstein barycenters. To provide suitable instances of such functionals, we
revisit Souslin space theory, Dunford-Pettis theorem and the de la Vall\'ee
Poussin criterion for uniform integrability. Our method shows that if a
probability measure $\mathbb{P}$ on $\mathcal{W}_2(M)$ gives mass to absolutely
continuous measures on $M$, then its unique barycenter is also absolutely
continuous. This generalizes the previous results on compact manifolds by Kim
and Pass arXiv:1412.7726 [math.AP] .
