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Abstract: We introduce the real space correlation function of $B$-mode polarization ofthe cosmic microwave background CMB as a probe of superhorizon tensorperturbations created by inflation. By causality, any non-inflationarymechanism for gravitational wave production after reheating, like global phasetransitions or cosmic strings, must have vanishing correlations for angularseparations greater than the angle subtended by the particle horizon atrecombination, i.e. $\theta \gtrsim 2^\circ$. Since ordinary $B$-modes aredefined non-locally in terms of the Stokes parameters $Q$ and $U$ and thereforedon-t have to respect causality, special care is taken to define `causal$\tilde B$-modes- for the analysis. We compute the real space $\tilde B$-modecorrelation function for inflation and discuss its detectability onsuperhorizon scales where it provides an unambiguous test of inflationarygravitational waves. The correct identification of inflationary tensor modes iscrucial since it relates directly to the energy scale of inflation. Wronglyassociating tensor modes from causal seeds with inflation would imply anincorrect inference of the energy scale of inflation. We find that thesuperhorizon $\tilde B$-mode signal is above cosmic variance for the angularrange $2^\circ < \theta < 4^\circ$ and is therefore in principle detectable. Inpractice, the signal will be challenging to measure since it requiresaccurately resolving the recombination peak of the $B$-mode power spectrum.However, a future CMB satellite CMBPol, with noise level $\Delta P \simeq1\mu$K-arcmin and sufficient resolution to efficiently correct forlensing-induced $B$-modes, should be able to detect the signal at more than3$\sigma$ if the tensor-to-scalar ratio isn-t smaller than $r \simeq 0.01$.

Autor: Daniel Baumann, Matias Zaldarriaga


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