Genus topology and cross-correlation of BICEP2 and Planck 353 GHz B-modes: further evidence favouring gravity wave detection

We have analysed the genus topology of the BICEP2 B-modes and found 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 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 similar in 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 per cent (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 per cent with a BICEP2 gravity wave signal with an rms amplitude equal to 54 per cent 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.