Missing baryons, bulk flows, and the E-mode polarization of the Cosmic Microwave Background

Most of the missing baryons are found in slightly overdense structures like filaments and superclusters, but to date most of them have remained hidden to observation. At the same time, the linear cosmological perturbation theory predicts the existence of extended bulk flows seeded by the gravitational attraction of linear potential wells, but again these also remain undetected. If the peculiar motion of galaxy groups and clusters indeed resembles that of the surrounding baryons, then the kinetic Sunyaev-Zel'dovich (kSZ) pattern of those massive halos should be closely correlated to the kSZ pattern of all surrounding electrons. Likewise, it should also be correlated to the CMB E-mode polarization field generated via Thomson scattering after reionization. We explore the cross-correlation of the kSZ generated in groups and clusters to the all sky E-mode polarization in the context of future CMB experiments like Planck, ACT, SPT or APEX. We find that this cross-correlation effectively probes redshifts below z = 3-4 (where most of the baryons cannot be seen), and that it arises on very large scales (l < 10). The significance with which this cross-correlation can be measured depends on the Poissonian uncertainty associated with the number of halos where the kSZ is measured and on the accuracy of the kSZ estimations themselves. Assuming that Planck can provide a cosmic variance limited E-mode polarization map at l < 20 and S/N similar to 1 kSZ estimates can be gathered for all clusters more massive than 10(14) M circle dot, then this cross-correlation should be measured at the 2-3 sigma level. Further, if an all-sky ACT or SPT type CMB experiment provides similar kSZ measurements for all halos above 10(13) M circle dot, then the cross-correlation total signal to noise (S/N) ratio should be at the level of 4-5. A detection of this cross-correlation would provide direct and definite evidence of bulk flows and missing baryons simultaneously.