Massless (pseudo-)scalar seeds of CMB anisotropy

A primordial stochastic background of very weakly coupled massless (pseudo-)scalars can seed CMB anisotropy, when large-scale fluctuations of their stress-tensor re-enter the horizon during the matter-dominated era. A general relation between multipole coefficients of the CMB anisotropy and the seed's energy spectrum is derived. Magnitude and tilt of the observed anisotropies can be reproduced for the nearly scale-invariant axion spectra that are predicted in a particularly symmetric class of string cosmology backgrounds.