A variable speed of light (VSL) cosmology is developed with a spontaneous breaking of Lorentz invariance in the early universe. A non-minimal electromagnetic coupling to curvature and the resulting quantum electrodynamic vacuum polarization dispersive medium can produce c >> c0 in the early universe, where c0 is the measured speed of light today. Higher derivative curvature contributions to the effective gravitational action and quantum gravity vacuum polarization can produce a dispersive medium and a large increase in the speed of gravitational waves cg >> cg0 in the early universe, where cg0 is the speed of gravitational waves today. The initial value problems of cosmology are solved: the horizon and flatness problems. The model predicts primordial scalar and tensor fluctuation spectral indices ns=0.96 and nt=- 0.04, respectively. The BICEP2 observation of r=0.2 yields r/nt=-5 which is close to the single-field inflationary consistency condition r/nt=-8.