Balancing bias, baryons, and scale cuts in LSST 3x2pt analysis

Abstract: Stage IV surveys such as LSST will probe deeply into the nonlinear regime, where systematic effects from galaxy bias and baryonic feedback become dominant and poorly constrained nuisance parameters can lead to degeneracies. In this work we present a $3\times2$pt analysis for LSST Y1 and Y10 data using the BACCO emulator for modelling both the hybrid-effective field theory (HEFT) for nonlinear galaxy bias and the baryonic feedback using the baryonification mechanism. We aim to find a balance between model complexity and scale cuts, with particular attention to parameter degeneracies and baryonic feedback effects on the galaxy--matter and galaxy--galaxy power spectra. First, we find that a linear bias model delivers percent-level, unbiased constraints on $Ω{\rm m}$ and $σ_8$ only up to $k{\rm max}=0.1\,h/$Mpc, but pushing to smaller scales requires a perturbative approach. Second, we compare HEFT with a minimal bias variant with fixed higher-order terms, and find that the latter is unbiased in $Λ$CDM even at $k_{\rm max}=0.7\,h/$Mpc. We show that higher-order bias can mimic baryonic suppression, but baryons cannot reproduce the full range of higher-order bias behaviour. Third, we find that a detection of the total neutrino mass $M_ν$ is possible for both Y1 and Y10 for $k\geq0.3\,h/$Mpc, at least when photo-$z$ uncertainties and related nuisance parameters are precisely known. However, the specific measured value is not robust across equally plausible mock scenarios: the inferred $M_ν$ can be significantly biased by adopting the minimal bias model. The entire analysis is conducted with a new independent, open source pipeline (MGL) that we present for the first time in this work.

• The paper demonstrates how choosing appropriate scale cuts and bias models (linear, HEFT, and minimal) is crucial for unbiased estimates of Ωm, σ8, and neutrino mass.
• It quantitatively shows that degeneracies between higher-order bias parameters and baryonic feedback can mimic power spectrum suppression at quasi-nonlinear scales.
• The study emphasizes the need for careful model validation and simulation-based priors to robustly extract cosmological information from LSST 3×2pt analyses.

Balancing Model Complexity and Scale Selection in LSST 3×2pt Cosmological Analyses

Background and Motivation

The LSST and other Stage IV photometric sky surveys will fundamentally advance precision cosmology through high signal-to-noise measurements of large-scale structure (LSS) via joint weak lensing and galaxy clustering statistics. The $3\times2$pt (three two-point correlation function) approach—galaxy clustering auto-correlation, gravitational shear (cosmic shear) auto-correlation, and their cross-correlation—offers significant power by simultaneously mitigating parameter degeneracies and calibrating key systematics (e.g., galaxy bias, intrinsic alignments, photometric redshifts).

A critical challenge for extracting unbiased cosmological information from next-generation surveys arises from the nonlinear regime. At high $k$, baryonic feedback and nonlinear galaxy bias become dominant and degenerate, with nuisance parameter dependence and weak external priors, especially as analyses push to smaller scales ($k \gtrsim 0.1\,h$/Mpc). The selection of scale cuts and complexity of the phenomenological model (especially the treatment of baryons and bias) thus controls both cosmological constraining power and the risk of bias.

Methodology

This work performs detailed forecast analyses for LSST Y1 and Y10, focusing on 1) the trade-off between scale cuts and model complexity, 2) the interplay of higher-order galaxy bias with baryonic suppression, and 3) the detection prospects for the total neutrino mass $M_\nu$. The pipeline leverages the BACCO emulator for nonlinear (matter and galaxy) power spectra, enabling hybrid effective field theory (HEFT) modeling for galaxy bias up to $k=0.7\,h$/Mpc, combined with baryonification-based baryonic feedback as parameterized in the BACCO framework.

Model variations considered include:

• Linear bias model: Only $b_1$ free, valid strictly for $k < 0.1\,h$/Mpc.
• HEFT: Full perturbative expansion including four bias terms per redshift bin.
• Minimal bias model: Higher-order bias parameters ($b_{s^2}$, $b_{\nabla^2}$) fixed to zero, motivated by typical small values in realistic galaxy populations.

Mock LSST Y1 and Y10 data vectors are produced, including redshift distributions (Figure 1).

Figure 1: Redshift distributions of the tomographic bins for lens and source samples as specified by the LSST-DESC Y1 and Y10 configurations.

Nuisance parameter combinations and baryonic suppression are varied systematically in the analyses, with forecast performance quantified using the Figure of Merit (FoM; inverse posterior volume for selected parameters) and Figure of Bias (FoB; Mahalanobis distance from true parameter to posterior mean).

Performance of Bias Models and Baryon Complexity

Linear vs. Higher-Order Bias

Comparisons demonstrate that the linear bias model yields unbiased $\Omega_{\rm m}$ and $k$0 estimates (FoB $k$1) only for conservative scale cuts $k$2/Mpc. Extension to smaller scales with linear bias incurs significant (up to 2$k$3) biases due to unmodeled higher-order bias effects and baryon degeneracies (Figure 2).

Figure 2: Figure of merit (FoM, top) and figure of bias (FoB, bottom) for $k$4 and $k$5 at different scale cuts, contrasting bias models with/without explicit baryonic feedback.

Adopting the minimal bias model recovers most of the benefit of HEFT without the computational and statistical implications of a large number of nuisance parameters. In LSST Y1/Y10, FoM and FoB using the minimal bias model track HEFT closely to the scale cut of $k$6/Mpc for typical galaxy populations—though this is sensitive to underlying bias parameter values.

Degeneracy Between Higher-Order Bias and Baryons

There is substantial degeneracy between the baryonic suppression of the nonlinear power spectrum and the effects of higher-order bias parameters. HEFT perturbative bias can mimic a broad range of baryonic-induced suppressions on angular clustering power spectra, as quantified in Figure 3.

Figure 3: Effects of baryonic suppression (pink shaded region) and higher-order bias parameters (gradient lines, HEFT) on galaxy-galaxy auto-correlation angular power spectra; both can yield similar phenomenology up to $k$7/Mpc.

Quantitative fits suggest that for nearly all physically reasonable baryonic suppression histories, some choice of higher-order bias parameters can yield an effectively indistinguishable $k$8, within $k$91% accuracy. However, baryons alone cannot reproduce all possible bias expansions.

Parameter Recovery and Model Mismatch

Across mock data scenarios, the minimal bias model generally recovers unbiased $k \gtrsim 0.1\,h$0 and $k \gtrsim 0.1\,h$1 when underlying higher-order bias terms are small. However, in scenarios where $k \gtrsim 0.1\,h$2, $k \gtrsim 0.1\,h$3, or $k \gtrsim 0.1\,h$4 are larger, the minimal model can yield significant shifts in derived $k \gtrsim 0.1\,h$5, even when $k \gtrsim 0.1\,h$6, $k \gtrsim 0.1\,h$7 are unbiased (Figure 4).

Figure 4: Posterior means and credible intervals for $k \gtrsim 0.1\,h$8, $k \gtrsim 0.1\,h$9, $M_\nu$0 (baryonic feedback), $M_\nu$1 and $M_\nu$2 with various bias/baryon modeling assumptions; best-fit solutions shown for each setup.

This is important for constraining beyond-$M_\nu$3CDM parameters.

Neutrino Mass Detection and Systematic Modeling

A central outcome is that detection of nonzero $M_\nu$4 via $M_\nu$5pt requires inclusion of quasi-nonlinear modes ($M_\nu$6/Mpc); linear bias alone is inadequate. Both Y1 and Y10 achieve clear neutrino mass detection in this regime; however, the recovered value of $M_\nu$7 can exhibit $M_\nu$8 shifts if the bias model is misspecified (Figures 5 and 6).

Figure 5: Figure of merit (top) and figure of bias (bottom) for $M_\nu$9 and $k=0.7\,h$0 as a function of scale cut, shown for different bias model assumptions in Y10.

Figure 6: 2D posterior regions for cosmological and neutrino mass parameters, contrasting modeling choices and true/fitted bias values; dashed contours show impact of doubling higher-order bias in the mock data.

Thus, the apparent independence of traditional cosmological parameters from model complexity may not extend to new physics. Degeneracies between higher-order bias and $k=0.7\,h$1 can result in under- or over-estimation of neutrino mass, with the magnitude of bias dependent on the underlying galaxy bias properties.

Furthermore, comparisons of bias and neutrino effects on the power spectrum (Figure 7) show that changes to higher-order bias parameters can closely mimic the power suppression associated with massive neutrinos, further compounding degeneracy.

Figure 7: Galaxy-galaxy auto-correlation spectrum at $k=0.7\,h$2 in bin 5 of Y10 showing how bias parameters can mimic the effect of massive neutrinos. Pink: high bias, no neutrinos; blue: standard bias, nonzero $k=0.7\,h$3.

Robustness, Limitations, and Pipeline Validation

The results hold for both LSST Y1 and Y10, with Y10 achieving approximately a factor of two improvement in constraining power for standard parameters. Modest degradation of cosmological constraints occurs with the inclusion of baryonic parameters (a factor of two in FoM), but minimal bias suffices for unbiased parameter recovery except where bias properties are significantly mismatched.

A new Bayesian inference pipeline (MGL) is introduced and benchmarked, showing consistency with DESC CCL-based analyses to well within numerical uncertainty (Figure 8).

Figure 8: Difference between $k=0.7\,h$4 predictions from CCL and MGL pipelines, weighted by $k=0.7\,h$5 errors; differences lie well within the accuracy target for all relevant scales.

Implications and Future Directions

The analysis demonstrates that for LSST-like data,

• Conservative scale cuts with a linear bias model yield robust standard parameter inference, but for maximal cosmological utility (including neutrino physics), quasi-nonlinear scales and a perturbative bias model are essential.
• Model complexity can be reduced to the minimal bias approach without degrading most parameter constraints, for "typical" galaxy populations. However, this is not guaranteed for all bias realizations, especially for constraints on $k=0.7\,h$6 or alternative cosmologies.
• Degeneracies between baryonic effects and galaxy bias are substantial and must be rigorously marginalized when utilizing scales $k=0.7\,h$7/Mpc.

The evident degeneracies require that careful validation against simulations and real galaxy samples be conducted before minimal bias modeling can be adopted safely. Further, the entire analysis assumes perfectly known photometric redshift distributions and exclusion of other systematics, which may further degrade parameter constraints or exacerbate degeneracies in practice.

Conclusion

A systematic, emulator-driven $k=0.7\,h$8pt analysis for LSST indicates that judicious selection of scale cuts and bias model complexity is critical to balancing constraining power with susceptibility to bias. The hybrid (HEFT or minimal) perturbative galaxy bias approach enables inclusion of non-linear scales ($k=0.7\,h$9/Mpc) and yields improved cosmological constraints for both standard and extended cosmological parameters, provided the underlying galaxy bias is representative. However, higher-order bias-baryon-neutrino degeneracies require that any minimal model be validated on a case-by-case basis, particularly for new physics searches.

Unambiguous detection of nonzero neutrino mass is feasible in LSST Y10 given these strategies, but robust inference of $b_1$0 significance and value will remain model dependent. Future directions include incorporating additional systematics, cross-survey analyses, and simulation-based priors on galaxy bias parameters to further mitigate degeneracies and improve robustness.