  Many recent experiments investigated potential and attractive means of
modifying many-body interactions in two-dimensional materials through
time-resolved spectroscopy techniques. However, the role of ultrafast
phonon-assisted processes in two-dimensional systems is rarely discussed in
depth. Here, we investigate the role of electron-phonon interaction in the
transient optical absorption of graphene by means of first-principles methods.
It is shown at equilibrium that the phonon-assisted transitions renormalize
significantly the electronic structure. As a result, absorption peak around the
Van Hove singularity broadens and redshifts by around 100\,meV. In addition,
temperature increase and chemical doping are shown to notably enhance these
phonon-assisted features. In the photoinduced transient response we obtain
spectral changes in close agreement with the experiments, and we associate them
to the strong renormalization of occupied and unoccupied $\pi$ bands, which
predominantly comes from the coupling with the zone-center $E_{2g}$ optical
phonon. Our estimation of the Coulomb interaction effects shows that the
phonon-assisted processes can have a dominant role even in the subpicosecond
regime.
