Comparing cosmic shear nulling methods for Stage-IV surveys

TL;DR

The paper addresses biases in cosmic shear from baryon feedback and evaluates three nulling strategies—LU nulling on the lensing data vector, the BNT transform on the shear field, and cross-correlation with low‑redshift LSS tracers—using a $k$‑cut extension and a Fisher forecast on a Euclid‑like mock. LU nulling reshapes the Limber integral via LU decomposition to suppress high‑$k$ modes; BNT reweights tomographic bins to sharpen the relation between angular and 3D space; cross‑correlation decorrelates shear from foreground density to damp low‑redshift contributions. The findings show that all three methods reduce biases on $S_8$ and $w_0,w_a$, with LUnul being the most aggressive in reducing bias at the cost of precision, BNT preserving more information and offering solid theoretical grounding, and cross‑correlation delivering strong bias reduction but requiring additional clustering data. Collectively, these results provide practical guidance for Stage‑IV analyses to mitigate baryonic uncertainties while preserving cosmological information, though some scale dependence and methodological tradeoffs remain depending on binning, $k_{ m max}$, and data availability.

Abstract

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.

Figures (11)

• Figure 1: Redshift distributions for six tomographic bins, which are used to produce mock power spectra. For the case of the cross-correlation method we take the two lowest redshift bins as our lens sample and the three highest redshift bins as our source sample, ignoring the third redshift bins to minimise overlap between the lens and source sample.
• Figure 2: The top panel shows the lensing kernels, $q^i(z)$ for the six tomographic bins shown in Figure \ref{['fig:nz']}, and the lower panel shows the BNT transformed lensing kernels, $\hat{q}^a(z)$. These distributions have been normalised to have the same peak value.
• Figure 3: Suppression of the matter power spectrum due to baryon feedback ($\Theta_{\rm AGN}=7.8$) at different redshifts.
• Figure 4: Impact of baryon feedback, assuming $\Theta_{\rm AGN}=7.8$, on the cosmic shear power spectra for the 'standard' case (orange), the BNT transformed case (blue) and the cross-correlation case (red). In all but the (0,0) bin pair, the BNT transformed spectra is less impacted by baryons, particularly considering higher redshift bin pairs. The cross-correlation-modified spectra are least impacted by baryons for the highest redshift bin pairs where the separation between lenses and sources is greatest. When there is more overlap between the bins the suppression due to baryons is increased at intermediate $$ compared to the standard case.
• Figure 5: Power spectra for each pair of tomographic bins including contribution from different ranges in $k$: the dashed line corresponds to the smallest scales with contributions from $k>0.5h/{\rm Mpc}$, the solid line corresponds to slightly larger scales $(0.1<k<0.5)h/{\rm Mpc}$ and the dotted line shows the full spectra including all $k$. The 'standard' case (orange) shows small scales contribute to even the smallest $$-modes, whilst the BNT-transformed spectra (blue) have a more direct mapping between $k$ and $$, especially for the higher redshift bins. The cross-correlation-modified spectra (red, highest three source bins only) exhibit a damping of the contribution from small scales relative to the 'standard' cosmic shear spectra; this is most significant in the highest redshift bin which has the largest separation to the lens sample. In the cross-correlation case there are 'wiggles' visible in the range $(0.1 < k < 0.5)h/{\rm Mpc}$ (red solid line) which come from the first lens bin and is due to the presence of the BAO in the clustering signal.