Novel cosmological tests from combining galaxy lensing and the polarized Sunyaev-Zel’dovich effect

The polarized Sunyaev-Zel’dovich (pSZ) effect is sourced by the Thomson scattering of CMB photons from distant free electrons and yields a novel view of the CMB quadrupole throughout the observable Universe. Galaxy shear measures the shape distortions of galaxies, probing both their local environment and the intervening matter distribution. Both observables have been shown to give interesting constraints on the cosmological model; in this work we ask: what can be learnt from their combination? The pSZ-shear cross-spectrum measures the shear-galaxy-polarization bispectrum ( i.e. (cid:104) γδ g ( Q ± iU ) (cid:105) ) and contains contributions from three main phenomena: (1) the Sachs-Wolfe (SW) effect, (2) the integrated Sachs-Wolfe (ISW) effect, (3) inflationary gravitational waves. Since the modes contributing to the pSZ signal are not restricted to the Earth’s past lightcone, the low-redshift cross-spectra could provide a novel constraint on dark energy properties via the ISW effect, whilst the SW signal is sourced by a coupling of scalar modes at very different times (recombination and the lensing redshift), but at similar positions; this provides a unique probe of the Universe’s homogeneous time evolution. We give expressions for all major contributions to the galaxy shear, galaxy density, and pSZ auto- and cross-spectra, and evaluate their detectability via Fisher forecasts. Despite significant theoretical utility, the shear cross-spectra will be challenging to detect: combining CMB-S4 with the Rubin observatory yields a 1 . 6 σ detection of the ISW contribution, though this increases to 5 . 2 σ for a futuristic experiment involving CMB-HD and a higher galaxy sample density. For parity-even (parity-odd) tensors, we predict a 1 σ limit of σ ( r ) = 0 . 9 (0 . 2) for CMB-S4 and Rubin, or 0 . 3 (0 . 06) for the more futuristic setup. Whilst this is significantly better than the constraints from galaxy shear alone (and contains fewer systematics than most auto-spectra), it is unlikely to be competitive, but may serve as a useful cross-check.