Robust cosmic shear with small-scale nulling

Standard cosmological weak lensing analyses using cosmic shear are inevitably sensitive to small-scale, non-linear clustering from low-redshift structures. The need to adequately model the clustering of matter on this non-linear regime, accounting for both gravitational and baryonic effects, adds significant uncertainty to weak lensing studies, particularly in the context of near-future Stage-IV datasets. In this paper, inspired by previous work on so-called ``nulling'' techniques, we present a general method that selects the linear combinations of a given tomographic cosmic shear dataset that are least sensitive to small-scale non-linearities, by essentially suppressing the contribution from low-redshift structures. We apply this method to the latest public cosmic shear data from the Dark Energy Survey, DES-Y3, that corresponds to 3 years of observation, and show: a) that a large fraction of the signal is dominated by the single mode that is most affected by non-linear scales, and b) that removing this mode leads to a $\sim1\sigma$ upwards shift in the preferred value of $S_8\equiv\sigma_8\sqrt{\Omega_M/0.3}$, alleviating the tension with current CMB data. However, the removal of the most contaminated mode also results in a significant increase in the statistical uncertainties. Taking this into account, we find this shift to be compatible with a random fluctuation caused by removing this most-contaminated mode at the $\sim1.4\sigma$ level. We also show that this technique may be used by future Stage-IV surveys to mitigate the sensitivity of the final constraints to baryonic effects, trading precision for robustness.