  We investigate the gravitational anomaly vertex $\langle TTJ_5\rangle$
(graviton - graviton - axial current) under conditions of finite density and
temperature. Through a direct analysis of perturbative contributions, we
demonstrate that neither finite temperature nor finite fermion density affects
the gravitational chiral anomaly. These results find application in several
contexts, from topological materials to the early universe plasma. They affect
the decay of any axion or axion-like particle into gravitational waves, in very
dense and hot environments.
