How to detect gravitational waves through the cross-correlation of the galaxy distribution with the CMB polarization

Understand

Thompson scattering of cosmic microwave background (CMB) photons off of free electrons during the reionization epoch induces a correlation between the distribution of galaxies and the polarization pattern of the CMB, the magnitude of which is proportional to the quadrupole moment of radiation at the time of scattering.

• Since the quadrupole moment generated by gravitational waves (GWs) gives rise to a different polarization pattern than that produced by scalar modes, one can put interesting constraints on the strength of GWs on large scales by cross-correlating the small scale galaxy distribution and CMB polarization.
• We use this method together with Fisher analysis to predict how well future surveys can measure the tensor-to-scalar ratio $r$.
• We find that with a future CMB experiment with detector noise Delta_P = 2 mu K-arcmin and a beam width theta_FWHM = 2' and a future galaxy survey with limiting magnitude I<25.6 one can measure the tensor-to-scalar ratio with an error sigma_r \simeq 0.09.