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 (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.
