  Cluster dynamical mean field methods are used to calculate the
superconductivity-induced changes in the interplane conductivity and Raman
scattering cross section of the two dimensional Hubbard model. When
superconductivity emerges from the pseudogap, the superconducting response is
found to be diminished in amplitude, broadened and, in the case of the
interplane conductivity, shifted to higher frequency. The results are in
agreement with data on high temperature copper-oxide superconductors indicating
that the Hubbard model contains the essential low energy physics of the
pseudogap and its interplay with superconductivity in the cuprates.
