  Given observations of B-mode polarization power spectrum of the cosmic
microwave background (CMB), we can reconstruct power spectra of primordial
tensor modes from the early Universe without assuming their functional form
such as a power-law spectrum. Shape of the reconstructed spectra can then be
used to probe the origin of tensor modes in a model-independent manner. We use
the Fisher matrix to calculate the covariance matrix of tensor power spectra
reconstructed in bins. We find that the power spectra are best reconstructed at
wavenumbers in the vicinity of $k\approx 6\times 10^{-4}$ and $5\times
10^{-3}~{\rm Mpc}^{-1}$, which correspond to the "reionization bump" at
$\ell\lesssim 6$ and "recombination bump" at $\ell\approx 80$ of the CMB B-mode
power spectrum, respectively. The error bar between these two wavenumbers is
larger because of lack of the signal between the reionization and recombination
bumps. The error bars increase sharply towards smaller (larger) wavenumbers
because of the cosmic variance (CMB lensing and instrumental noise). To
demonstrate utility of the reconstructed power spectra we investigate whether
we can distinguish between various sources of tensor modes including those from
the vacuum metric fluctuation and SU(2) gauge fields during single-field
slow-roll inflation, open inflation and massive gravity inflation. The results
depend on the model parameters, but we find that future CMB experiments are
sensitive to differences in these models. We make our calculation tool
available on-line.
