Causality and Primordial Tensor Modes
  We introduce the real space correlation function of $B$-mode polarization of
the cosmic microwave background (CMB) as a probe of superhorizon tensor
perturbations created by inflation. By causality, any non-inflationary
mechanism for gravitational wave production after reheating, like global phase
transitions or cosmic strings, must have vanishing correlations for angular
separations greater than the angle subtended by the particle horizon at
recombination, i.e. $\theta \gtrsim 2^\circ$. Since ordinary $B$-modes are
defined non-locally in terms of the Stokes parameters $Q$ and $U$ and therefore
don't have to respect causality, special care is taken to define `causal
$\tilde B$-modes' for the analysis. We compute the real space $\tilde B$-mode
correlation function for inflation and discuss its detectability on
superhorizon scales where it provides an unambiguous test of inflationary
gravitational waves. The correct identification of inflationary tensor modes is
crucial since it relates directly to the energy scale of inflation. Wrongly
associating tensor modes from causal seeds with inflation would imply an
incorrect inference of the energy scale of inflation. We find that the
superhorizon $\tilde B$-mode signal is above cosmic variance for the angular
range $2^\circ < \theta < 4^\circ$ and is therefore in principle detectable. In
practice, the signal will be challenging to measure since it requires
accurately resolving the recombination peak of the $B$-mode power spectrum.
However, a future CMB satellite (CMBPol), with noise level $\Delta_P \simeq
1\mu$K-arcmin and sufficient resolution to efficiently correct for
lensing-induced $B$-modes, should be able to detect the signal at more than
3$\sigma$ if the tensor-to-scalar ratio isn't smaller than $r \simeq 0.01$.
