  The interaction of excitons with lattice vibrations underlies the scattering
from bright to dark excitons as well as the coherent modulation of the exciton
energy. Unlike the former mechanism, which involves phonons with finite
momentum, the latter can be exclusively attributed to {\it coherent phonons}
with zero momentum. We here lay down the microscopic theory of coherent phonons
interacting with resonantly pumped bright excitons and provide the explicit
expression of the corresponding coupling. The coupling notably resembles the
exciton-phonon one, but with a crucial distinction: it contains the bare
electron-phonon matrix elements rather than the screened ones. Our theory
predicts that the exciton energy features a polaronic-like red-shift and
monochromatic oscillations or beatings, depending on the number of coupled
optical modes. Both the red-shift and the amplitude of the oscillations are
proportional to the excitation density and to the square of the
exciton-coherent-phonon coupling. We validate our analytical findings through
comparisons with numerical simulations of time-resolved optical absorbance in
resonantly pumped MoS$_{2}$ monolayers.
