  A large set of independent astronomical observations have provided a strong
evidence for nonbaryonic dark matter in the Universe. One of the most
investigated candidates is an unknown long-lived Weakly Interacting Massive
Particle (WIMP) which was in thermal equilibrium with the primeval plasma. Here
we investigate the WIMP abundance based on the relativistic kinetic treatment
for gravitationally induced particle production recently proposed in the
literature (Lima \& Baranov, Phys. Rev. D {\bf 90}, 043515, 2014). The new
evolution equation is deduced and solved both numerically and also through a
semi-analytical approach. The predictions of the WIMP observables are discussed
and compared with the ones obtained in the standard approach.
