  Topological changes of the Fermi surface under pressure may cause anomalies
in the low-temperature elastic properties. Our density functional calculations
for elemental Osmium evidence that this metal undergoes three such Lifshitz
transitions in the pressure range between 70 GPa and 130 GPa. The related
elastic anomalies are, however, invisibly weak. The critical pressures
considerably exceed the values for recently measured and calculated anomalies
in the pressure (P) dependence of the hexagonal c/a lattice parameter ratio
close to 25 GPa. We demonstrate that the latter anomalies are statistically not
significant and that (c/a)(P) can be fitted equally well by a smooth
dependence.
