  In the charge-ordered phase of strongly doped manganites
La$_{1-x}$Ca$_x$MnO$_3$ ($x \geq 0.5$) absorption lines appear in the terahertz
spectral range for commensurate $x$ values right below the charge-ordering
temperature. They are connected to acoustic phonons that become optically
active by folding of the Brillouin zone. At lower temperatures a strongly
asymmetric extra absorption band develops at frequencies corresponding to the
position of the lowest-energy van Hove singularity in the reduced Brillouin
zone. The band is assigned to the boson peak, i.e. to the excess of lattice
vibrational states over the standard Debye contribution. The folded phonons and
the boson peak do not show up for incommensurate calcium contents when no
distinct Brillouin zone folding exists.
