Eigen reconstruction of perturbations to the primordial tensor power spectrum

We explore the potential of the B-mode anisotropies of the cosmic microwave background radiation to constrain the shape of the primordial tensor power spectrum in a model-independent way. We expand possible perturbations to the power-law primordial tensor spectrum (predicted by the simplest single-field, slow-roll inflationary models) using various sets of localized and nonlocalized basis functions and construct the Fisher matrix for their amplitudes. The eigen analysis of the Fisher matrix would then yield a hierarchy of uncorrelated perturbation patterns (called tensor eigenmodes or TeMs), which are rank-ordered according to their measurability by data. We find that the first three TeMs are expected to be constrainable within a few percent by the next generation of B-mode experiments. We discuss how the method can be iteratively used to reconstruct the observable part of any general deviation from the fiducial power spectrum.