  In the inflationary scenarios suggested by string theory, the vacuum
fluctuations of the electromagnetic field can be amplified by the
time-evolution of the dilaton background, and can grow large enough to explain
both the origin of the cosmic magnetic fields and of the observed CMB
anisotropy. The normalization of the perturbation spectrum is fixed, and
implies a relation between the perturbation amplitude at the COBE scale and the
spectral index $n$. Working within a generic two-parameter family of
backgrounds, a large scale anisotropy $\Delta T/T\simeq 10^{-5}$ is found to
correspond to a spectral index in the range $n\simeq 1.11 - 1.17$.
