Can weak lensing surveys confirm BICEP2?

The detection of B-modes in the cosmic microwave background (CMB) polarization by the BICEP2 experiment, if interpreted as evidence for a primordial gravitational wave background, has enormous ramifications for cosmology and physics. It is crucial to test this hypothesis with independent measurements. A gravitational wave background leads to B-modes in galaxy shape correlations (shear) both through lensing and tidal alignment effects. Since the systematics and foregrounds of galaxy shapes and CMB polarization are entirely different, a detection of a cross correlation between the two observables would provide conclusive proof for the existence of a primordial gravitational wave background. We find that upcoming weak lensing surveys will be able to detect the cross correlation between B-modes of the CMB and galaxy shapes. However, this detection is not sufficient to confirm or falsify the hypothesis of a primordial origin for CMB B-mode polarization.

Figure 1

The B-mode autopower spectrum of galaxy shapes at $z=\{0.8,2,4\}$, from bottom to top. The blue lines show the contribution of alignments and lensing, while the black lines show the contribution of lensing alone. Alignments due to primordial tensor modes dominate the power spectrum.

Figure 2

Cross-correlation coefficient of shear and CMB B-modes as a function of multipole moment and at redshifts $z=0.5$ (blue), $z=1$ (red) and $z=2$ (black).

Figure 3

The significance for ruling out foregrounds [red curve, Eq. (12)] and for ruling out $r=0$ [dashed blue curve, Eq. (11)]. This is presented as a function of the projected number density of red galaxies in the survey for $r=0.2$ (top panel) and $r=0.02$ (bottom panel). We also present it as a function of shape noise, ${\sigma }_{\gamma }^2$ for a number density of ten galaxies per ${\mathrm{arcmin}}^2$ and $r=0.2$ in the middle panel. The black curve shows the corresponding significance for the detection of $C^{\gamma \gamma }(l)$. The blue dotted curve in the top panel shows the decrease in the significance for ruling out $r=0$ when the CMB noise is increased by a factor of 10.