Constraining primordial vector mode from B-mode polarization
  The B-mode polarization spectrum of the Cosmic Microwave Background (CMB) may
be the smoking gun of not only the primordial tensor mode but also of the
primordial vector mode. If there exist nonzero vector-mode metric perturbations
in the early Universe, they are known to be supported by anisotropic stress
fluctuations of free-streaming particles such as neutrinos, and to create
characteristic signatures on both the CMB temperature, E-mode, and B-mode
polarization anisotropies. We place constraints on the properties of the
primordial vector mode characterized by the vector-to-scalar ratio $r_{v}$ and
the spectral index $n_{v}$ of the vector-shear power spectrum, from the {\it
Planck} and BICEP2 B-mode data. We find that, for scale-invariant initial
spectra, the $\Lambda$CDM model including the vector mode fits the data better
than the model including the tensor mode. The difference in $\chi^{2}$ between
the vector and tensor models is $\Delta\chi^{2} = 3.294$, because, on large
scales the vector mode generates smaller temperature fluctuations than the
tensor mode, which is preferred for the data. In contrast, the tensor mode can
fit the data set equally well if we allow a significantly blue-tilted spectrum.
We find that the best-fitting tensor mode has a large blue tilt and leads to an
indistinct reionization bump on larger angular scales. The slightly red-tilted
vector mode supported by the current data set can also create ${\cal
O}(10^{-22})$-Gauss magnetic fields at cosmological recombination. Our
constraints should motivate research that considers models of the early
Universe that involve the vector mode.
