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We explore the potential of the B-mode anisotropies of the Cosmic Microwave Background radiation (CMB) 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.
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