A Consistency Relation for the CMB B-mode Polarization in the Squeezed
  Limit
  A large-scale temperature perturbation has a non-zero correlation with the
power spectrum of B-modes of cosmological origin on short scales while the
corresponding correlation is expected to be zero for B-modes sourced by
galactic foregrounds. We thus compute the squeezed limit of a three-point
function in which one correlates the temperature fluctuations at large scales
with two polarization modes at small scales. In the particular case of the
B-mode polarization we obtain a relation that connects the squeezed limit of
the $TBB$ three-point function with the cosmological B-mode power spectrum,
which can be used as a consistency relation. This could in principle help to
distinguish a primordial signal from that induced by inter-stellar dust.
