[Paper Review] Galaxy bias in the era of LSST: perturbative bias expansions

Andrina Nicola, Boryana Hadzhiyska+15 more|arXiv (Cornell University)|Jul 6, 2023

Galaxies: Formation, Evolution, PhenomenaPhysics and Astronomy3 citations

TL;DR

This paper evaluates nonlinear galaxy bias models for the Rubin Observatory's LSST Y10 survey using perturbative and effective field theory approaches. It finds that HEFT, LPT, and EPT models with non-perturbative matter power spectra yield unbiased cosmological constraints up to $k_{\mathrm{max}}=0.4\;\mathrm{Mpc}^{-1}$, even with assembly bias, and that small-scale clustering primarily improves bias, not cosmological, constraints.

ABSTRACT

Upcoming imaging surveys will allow for high signal-to-noise measurements of galaxy clustering at small scales. In this work, we present the results of the LSST bias challenge, the goal of which is to compare the performance of different nonlinear galaxy bias models in the context of LSST Y10 data. Specifically, we compare two perturbative approaches, Lagrangian perturbation theory (LPT) and Eulerian PT (EPT) to two variants of Hybrid Effective Field Theory (HEFT), with our fiducial implementation of these models including terms up to second order in the bias expansion as well as nonlocal bias and deviations from Poissonian stochasticity. We consider different simulated galaxy samples and test the performance of the bias models in a tomographic joint analysis of LSST-Y10-like galaxy clustering, galaxy-galaxy-lensing and cosmic shear. We find both HEFT methods as well as LPT and EPT combined with non-perturbative predictions for the matter power spectrum to yield unbiased constraints on cosmological parameters up to at least a maximal scale of $k_{\mathrm{max}}=0.4 \; \mathrm{Mpc}^{-1}$ for all samples considered, even in the presence of assembly bias. While we find that we can reduce the complexity of the bias model for HEFT without compromising fit accuracy, this is not generally the case for the perturbative models. We find significant detections of non-Poissonian stochasticity in all cases considered, and our analysis shows evidence that small-scale galaxy clustering predominantly improves constraints on galaxy bias rather than cosmological parameters. These results therefore suggest that the systematic uncertainties associated with current nonlinear bias models are likely to be subdominant compared to other sources of error for tomographic analyses of upcoming photometric surveys, which bodes well for future galaxy clustering analyses using these high signal-to-noise data. [abridged]

Motivation & Objective

• To assess the performance of nonlinear galaxy bias models in the context of LSST Year 10 (Y10) photometric clustering, lensing, and shear data.
• To compare perturbative models (LPT, EPT) and Hybrid Effective Field Theory (HEFT) variants in their ability to recover unbiased cosmological parameters.
• To investigate the impact of non-Poissonian stochasticity and nonlocal bias on cosmological constraints.
• To determine whether model complexity can be reduced without sacrificing accuracy, especially in the presence of assembly bias.
• To quantify the relative contribution of small-scale galaxy clustering to cosmological versus bias parameter constraints.

Proposed method

• Conduct a tomographic joint analysis of LSST-Y10-like galaxy clustering, galaxy-galaxy-lensing, and cosmic shear using simulated data from the AbacusSummit simulations.
• Implement four bias models: two HEFT variants (anzu and BACCO), and two perturbative approaches (LPT and EPT), all including second-order bias terms, nonlocal bias, and non-Poissonian stochasticity.
• Use non-perturbative matter power spectra (e.g., from N-body simulations) to improve the reach of perturbative models beyond their standard perturbative limits.
• Apply a Gaussian likelihood with rescaled covariance matrices to ensure consistent signal-to-noise across $P(k)$ and $C_\ell$ data, enabling cross-comparison.
• Perform single-bin and redshift-slice fits using spherical harmonic power spectra and three-dimensional $P(k)$, comparing bias and cosmological parameter constraints.
• Use Fisher matrix estimates at best-fit values (with $b_{s^2}=0$) to compare consistency across different data sets and fitting strategies.

Experimental results

Research questions

• RQ1 Can perturbative and HEFT-based bias models yield unbiased cosmological constraints up to $k_{\mathrm{max}}=0.4\;\mathrm{Mpc}^{-1}$ in LSST-Y10 data, even with assembly bias?
• RQ2 How does the inclusion of non-Poissonian stochasticity affect the performance of bias models and cosmological parameter recovery?
• RQ3 To what extent do small-scale galaxy clustering measurements improve constraints on galaxy bias versus cosmological parameters?
• RQ4 Can the complexity of HEFT and perturbative models be reduced without degrading fit accuracy, particularly in the presence of assembly bias?
• RQ5 Are results from spherical harmonic power spectra consistent with those from three-dimensional $P(k)$ analyses across redshift bins?

Key findings

• All four models—LPT, EPT, anzu-HEFT, and BACCO-HEFT—produce unbiased constraints on $\sigma_8$ and $\Omega_c$ up to $k_{\mathrm{max}}=0.4\;\mathrm{Mpc}^{-1}$, even when assembly bias is present.
• Non-Poissonian stochasticity is significantly detected in all simulated galaxy samples, indicating its importance in modeling small-scale clustering.
• Small-scale galaxy clustering primarily improves constraints on galaxy bias parameters rather than cosmological parameters, suggesting bias systematics are subdominant to other errors.
• HEFT models allow for reduced complexity without loss of accuracy, but this is not generally true for perturbative models (LPT/EPT), which require full complexity to maintain performance.
• The results from spherical harmonic $C_\ell$ analysis are consistent with those from three-dimensional $P(k)$ analysis and single-redshift fits, confirming internal consistency and robustness of the $C_\ell$ method.
• EPT shows significant bias in cosmological constraints for $k_{\mathrm{max}}\gtrsim 0.2\;\mathrm{Mpc}^{-1}$, indicating limitations in its reach compared to HEFT and LPT with non-perturbative matter spectra.