Abstract
In this paper, we thoroughly study the Ricci-Bourguignon almost soliton and gradient Ricci-Bourguignon almost soliton on paracontact metric manifolds. First we find some sufficient conditions under which a paracontact metric manifolds admitting a Ricci-Bourguignon almost soliton is Einstein (trivial). Next we prove that if a para-Sasakian manifold admits a gradient Ricci-Bourguignon almost soliton, it is Einstein (trivial) with constant scalar curvature - 2n(2n + 1). It is locally isometric to a flat manifold product and a manifold of constant curvature -4 if it is for (k, mu)-paracontact manifold admits a gradient Ricci-Bourguignon almost soliton.