Local primordial non-Gaussianity using cross-correlations of DESI tracers

1. Problem Statement

The primary goal of the paper is to constrain the amplitude of local primordial non-Gaussianity ($f_{\text{loc}}^{\text{NL}}$), a parameter describing deviations from a Gaussian distribution in the early universe's density fluctuations. A precise detection of $f_{\text{loc}}^{\text{NL}}$ (specifically at the level of $O(1)$) would rule out single-field inflation models.

While the Planck satellite provided the tightest constraints to date ($f_{\text{loc}}^{\text{NL}} = -0.9 \pm 5.1$), these are limited by cosmic variance on the 2D surface of last scattering. Large-scale structure (LSS) surveys offer a path to higher precision by measuring the scale-dependent bias induced by $f_{\text{loc}}^{\text{NL}}$ on biased tracers (galaxies and quasars) at high redshifts.

The Specific Challenge:
The Dark Energy Spectroscopic Instrument (DESI) Data Release 1 (DR1) includes Luminous Red Galaxies (LRGs), Quasars (QSOs), and Emission Line Galaxies (ELGs). However, the ELG sample suffers from severe imaging systematics at large scales (low $k$), which are the exact scales most sensitive to $f_{\text{loc}}^{\text{NL}}$. Previous analyses excluded ELGs from $f_{\text{loc}}^{\text{NL}}$ constraints because residual systematics could mimic or swamp the signal. The authors aim to include ELG information and improve constraints on LRGs and QSOs by utilizing cross-correlations between different tracer populations to mitigate these systematics.

2. Methodology

Data Samples

The analysis utilizes DESI DR1 LSS catalogs (version v1.5) covering the redshift range $0.4 < z < 3.1$. The samples include:

• Auto-tracers: LRGs ($0.4 < z < 1.1$), ELGs ($0.8 < z < 1.6$), and QSOs ($0.8 < z < 3.1$).
• Cross-tracers:
  • LRG $\times$ QSO ($0.8 < z < 1.1$)
  • ELG $\times$ LRG ($0.8 < z < 1.1$)
  • ELG $\times$ QSO ($0.8 < z < 1.6$)

Weighting and Systematics Mitigation

• Imaging Systematics: Weights ($w_{sys}$) are applied to correct for target density fluctuations correlated with imaging depth, seeing, etc. LRGs use linear regression; ELGs use the SYSNet neural network; QSOs use Regressis.
• Optimal Weighting: The authors apply FKP (Feldman-Kaiser-Peacock) weights to minimize variance. For QSOs, they also apply Optimal Quadratic Estimator (OQE) weights to account for redshift evolution in the scale-dependent bias.
• ELG Handling: Due to residual systematics, the ELG auto-power spectrum is conservatively cut at $k_{min} = 0.01 \, h \, \text{Mpc}^{-1}$, sacrificing precision to avoid bias. However, ELGs are included in cross-correlations where non-common systematics are expected to cancel out.

Analysis Framework

• Power Spectrum Measurement: Measured using pypower in Fourier space.
• Theoretical Model: The model incorporates the scale-dependent bias $\Delta b(k, z) \propto f_{\text{loc}}^{\text{NL}} / k^2$. The bias parameter $b_\phi$ is linked to the linear bias $b_1$ via a merger history parameter $p$.
  • $p=1$ for LRGs (mass universality).
  • $p=1.6$ for QSOs and ELGs (recent merger history).
• Integral Constraints: Radial (RIC) and Angular (AIC) integral constraints are modeled using EZmocks to correct for mode suppression caused by shuffling redshifts and systematics mitigation.
• Parameter Estimation: A likelihood analysis is performed using the desilike pipeline. The covariance matrix is constructed from 1000 EZmocks (effective Zel'dovich approximation mocks), corrected with Hartlap and Percival factors to account for noise in the covariance estimation.

3. Key Contributions

1. Validation of Cross-Correlations for PNG: The paper demonstrates that cross-correlating different tracers (e.g., LRG $\times$ QSO) effectively suppresses non-common systematics, allowing for robust constraints on $f_{\text{loc}}^{\text{NL}}$ even when one tracer (like ELGs) has significant residual systematics.
2. Inclusion of ELGs in PNG Analysis: It provides a framework for including ELGs in PNG constraints via cross-correlations (ELG $\times$ LRG, ELG $\times$ QSO), treating them as probes of the underlying $f_{\text{loc}}^{\text{NL}}$ signature rather than relying on their auto-power spectrum.
3. Systematic Error Estimation: By comparing constraints derived from different combinations of auto- and cross-correlations, the authors test for consistency. Discrepancies between different tracer combinations are used to quantify systematic uncertainties.
4. Mock-Based Expectation vs. Reality: The study rigorously compares DESI DR1 data results against EZmocks to determine if observed gains (or lack thereof) are statistically significant or consistent with cosmic variance and scatter.

4. Key Results

Constraints on $f_{\text{loc}}^{\text{NL}}$

• Baseline (LRG + QSO Auto): $f_{\text{loc}}^{\text{NL}} = -2.5^{+9.5}_{-9.4}$ (68% CL).
• With LRG $\times$ QSO Cross-Correlation: The constraint tightens to $f_{\text{loc}}^{\text{NL}} = 2.1^{+8.8}_{-8.3}$.
  • This represents a ~9% improvement in precision ($\sigma_{f_{\text{loc}}^{\text{NL}}}$ reduced from 9.33 to 8.54).
  • This result is consistent with the ~8% gain predicted by EZmocks.
• Including ELGs (Auto + Cross): Adding ELG auto, ELG $\times$ LRG, and ELG $\times$ QSO yields $f_{\text{loc}}^{\text{NL}} = -4.9^{+8.0}_{-9.6}$.
  • The precision ($\sigma \approx 8.64$) is nearly identical to the LRG $\times$ QSO case.
  • No significant gain was observed from adding ELGs to the DR1 dataset, likely due to the conservative $k_{min}$ cut and residual systematics.
  • However, mock tests predicted an ~8% additional gain from ELGs. The fact that the data did not show this gain is consistent with statistical scatter (28% of mocks showed a smaller gain).

Systematics and Consistency

• The central value shifted by $\sim 0.5\sigma$ when adding ELG cross-correlations, but this shift is well within the statistical fluctuations observed in the mock realizations.
• The results are robust against the choice of the assembly bias parameter $p$. Using updated values ($p=0.55$ for LRGs, $p=1.4$ for QSOs) yields $f_{\text{loc}}^{\text{NL}} = 1.9^{+7.6}_{-6.8}$, which is the tightest constraint from power spectra alone to date.

5. Significance and Conclusion

• Robust Improvement: The inclusion of the LRG $\times$ QSO cross-correlation is a robust method to improve $f_{\text{loc}}^{\text{NL}}$ constraints, offering a ~9% gain in precision for DESI DR1. This strategy is recommended for all future DESI PNG analyses.
• ELG Potential: While ELGs did not improve DR1 constraints due to current systematics and conservative cuts, the methodology validates their potential. Future data releases (DR2) with larger samples and better systematics mitigation are expected to realize the ~16% total gain predicted by mocks.
• Future Outlook: The authors plan to apply this full cross-correlation framework to DESI DR2 and the Year 5 (Y5) footprint, including full cross-covariances between QSOs and other tracers, which were approximated in this work.

In summary, this paper establishes a rigorous framework for using cross-correlations to mitigate systematics in $f_{\text{loc}}^{\text{NL}}$ measurements, successfully improving constraints on DESI DR1 data and paving the way for high-precision inflation tests with future data.