Searching for integrated Sachs–Wolfe effect beyond temperature anisotropies: CMB E-modepolarization–galaxy cross-correlation

Abstract

The cross-correlation between cosmic microwave background (CMB) temperatureanisotropies and the large-scale structure (LSS) traced by the galaxy distribution, orsources at different wavelengths, is now well known. This correlation results from theintegrated Sachs–Wolfe (ISW) effect in CMB anisotropies generated at late times due tothe dark energy component of the Universe. In a reionized universe, electron scattering atlow redshifts leads to a large-scale polarization contribution. In addition to theprimordial quadrupole, involving anisotropies at the last scattering surface, the ISWquadrupole rescatters and contributes to the large angular scale polarization signal.Thus, in principle, the low multipole polarization bump in the E-mode should becorrelated with the galaxy distribution. Unlike the CMB temperature–LSS correlationthat peaks for tracers at low redshifts, due to the increasing visibility function,while the fractional ISW quadrupole is decreasing, with increasing redshift, thepolarization–galaxy correlation peaks mostly at redshifts between 1 and 3. Under certainconditions, mostly involving a low optical depth to reionization if the Universereionized at a redshift around 6, the cross-polarization–source signal is marginallydetectable if all-sky maps of the large-scale structure at redshifts between 1 and 3 areavailable. If the Universe reionized at a redshift higher than 10, it is unlikely thatthis correlation will be detectable even with no instrumental noise all-sky maps.While our estimates do not guarantee a detection, unknown physics related tothe dark energy uncertain issues related to the large angular scale CMB andpolarization anisotropies, and uncertainties related to the reionization history of theUniverse may motivate attempts to measure this correlation using upcoming CMBpolarization E-mode maps and large-scale structure maps of the high-redshift universewith the Large Synoptic Survey Telescope and quasar catalogues, among others.