We describe experiments devised to detect a possible effect of annealing on the vibrational density of states (DOS) in a glassforming polymer with high accuracy from inelastic incoherent neutron scattering. Such an effect could be expected from the argument that annealing changes the behavior of many measured quantities, especially the specific heat c(p)(T). For the experiment polybutadiene was chosen because the effect on c(p)(T) as well as the optimal conditions of annealing are well known for this material. Contrary to our expectations an annealing effect could be detected neither in the inelastic spectra taken on IN6 nor in the elastic scans performed on IN16 at ILL, Grenoble. From this we conclude that the observed annealing effect on c(p)(T) does not originate from a difference in the DOS but rather from other sources, e.g, a change of configurational entropy. This result is in agreement with a theory of DiMarzio which gives a good prediction of the step Delta c(p) at the glass transition in the case of polybutadiene and attributes only 8%-10% of it to vibrational terms.