The role of collective modes in various experiments on the cuprates is investigated. We calculate the neutron scattering, photoemission (ARPES), and Raman scattering intensities below $T_c$ within the fluctuation-exchange (FLEX) approximation for the two-dimensional Hubbard model. It is shown that the large peak in the dynamical spin susceptibility arises from a weakly damped spin-density-wave collective mode. This gives rise to a dip between the sharp low energy peak and the higher binding energy hump in the ARPES spectrum. Furthermore, we show that the collective mode of the amplitude fluctuation of the d-wave gap yields a broad peak above the pair-breaking threshold in the $B_{1g}$ Raman spectrum.

to be published in Phys. Rev. B Nov. 1st