Is the Rees-Sciama effect detectable by the next generation of cosmological experiments?

Non-linear growth of structure causes the gravitational potentials to grow with time, and this leaves an imprint on the small-scale temperature fluctuations of the Cosmic Microwave Background (CMB), a signal known as the Rees-Sciama (RS) effect. Building on previous studies, here we investigate the detectability of the RS effect by cross-correlating upcoming CMB and Large-Scale Structure surveys. We include tracers with realistic number density and bias, realistic noise for upcoming and future CMB experiments, and importantly, the contribution from CMB foregrounds to the noise budget. We also derive optimal redshift weights, which are crucial to the detection due to the mismatch between the redshift kernel of the RS effect and the typical redshift distribution of current and upcoming galaxy surveys. In agreement with previous work, we confirm that the signal would in principle be detectable at high significance by "white noise" versions of future CMB experiments, when foregrounds are not included as part of the noise. However, we show that inclusion of foregrounds limits the statistical detectability of the signal: an optimally-weighted high-redshift sample from Rubin Observatory LSST, together with CMB maps from CMB-S4 or CMB-HD, can yield a detection with signal-to-noise 6 - 8, when taking $\ell_{\rm max} = 6000$, provided that foreground-induced biases can be successfully controlled. Improvements are possible if the total power from foregrounds is further reduced, for example by more aggressive masking, or if the signal can be modeled down to smaller scales.