Comparing cosmic shear nulling methods for Stage-IV surveys

We present an analysis comparing nulling strategies for reducing the impact of baryon feedback on cosmic shear measurements. We consider three different approaches which aim to `null' the high-$k$ modes using transformations applied to the data vector: the Bernardeau-Nishimichi-Taruya (BNT) transform which operates on the lensing field, a new implementation of an LU factorisation of the discretized Limber integral (LUnul) which operates on the lensing two-point statistics, and finally a method which uses a correlated LSS tracers to suppress contributions from lower redshifts (cross-correlation). We compare these methods to un-nulled (or standard) cosmic shear at the data vector level and assess whether these methods are able to reduce the bias on cosmological constraints using a Fisher forecast. We find that the nulling techniques considered can have a large impact on reducing the bias on $S_8$ and Dark Energy parameters. The cross-correlation method is effective at reducing biases in $S_8$, but requires additional information from galaxy clustering. The LUnul method is the most aggressive of the methods and hence reduces biases most efficiently as $k_{\rm max}$ is increased, although this improvement in accuracy comes at the cost of precision. The BNT approach preserves more information than LUnul, and has a more rigorous theoretical grounding. We demonstrate that all three of these methods are effective at mitigating bias, and can be readily applied in forthcoming lensing analyses.