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 $Λ$CDM model including the vector mode fits the data better than the model including the tensor mode. The difference in $χ^{2}$ between the vector and tensor models is $Δχ^{2} = 3.294$, 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.

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