Genus Topology and Cross-Correlation of BICEP2 and Planck 353 GHz
  B-Modes: Further Evidence Favoring Gravity Wave Detection
  We have analyzed the genus topology of the BICEP2 B-modes and find them to be
Gaussian random phase as expected if they have a cosmological origin. These
BICEP2 B-modes can be produced by gravity waves in the early universe, but some
question has arisen as to whether these B-modes (for 50 < l < 120) may instead
be produced by foreground polarized dust emission. The dust emission at 150 GHz
observed by BICEP2 should be less in magnitude but have similar structure to
that at 353 GHz. We have therefore calculated and mapped the B-modes in the
BICEP2 region from the publicly available Q and U 353 GHz preliminary Planck
polarization maps. These have a genus curve that is different from that seen in
the BICEP2 observations, with features at different locations from those in the
BICEP2 map. The two maps show a positive correlation coefficient of 15.2% +/-
3.9% (1-sigma). This requires the amplitude of the Planck (50 < l <120) dust
modes to be low in the BICEP2 region, and the majority of the Planck 353 GHz
signal in the BICEP2 region in these modes to be noise. We can explain the
observed correlation coefficient of 15.2% with a BICEP2 gravity wave signal
with an rms amplitude equal to 54% of the total BICEP2 rms amplitude. The
gravity wave signal corresponds to a tensor-to-scalar ratio r = 0.11 +/- 0.04
(1-sigma). This is consistent with a gravity wave signal having been detected,
at a 2.5-sigma level. The Planck and BICEP2 teams have recently engaged in
joint analysis of their combined data|it will be interesting to see if that
collaboration reaches similar conclusions.
