[Paper Review] Quijote PNG: The information content of the halo power spectrum and bispectrum

William R. Coulton, Francisco Villaescusa-Navarro+7 more|arXiv (Cornell University)|Jun 30, 2022

Galaxies: Formation, Evolution, Phenomena111 references36 citations

TL;DR

This study uses the Quijote-PNG N-body simulations to quantify how much primordial non-Gaussianity (PNG) can be constrained by small-scale halo power spectrum and bispectrum measurements. It finds that for local PNG, power spectrum measurements with sample variance cancellation provide tighter constraints than the bispectrum, while for equilateral and orthogonal PNG, the bispectrum on small scales (k ≤ 0.5 h/Mpc) enhances constraints by up to fourfold, primarily by breaking degeneracies with cosmological parameters.

ABSTRACT

We investigate how much can be learnt about four types of primordial non-Gaussianity (PNG) from small-scale measurements of the halo field. Using the QUIJOTE-PNG simulations, we quantify the information content accessible with measurements of the halo power spectrum monopole and quadrupole, the matter power spectrum, the halo-matter cross spectrum and the halo bispectrum monopole. This analysis is the first to include small, non-linear scales, up to $k_\mathrm{max}=0.5 \mathrm{h/Mpc}$, and to explore whether these scales can break degeneracies with cosmological and nuisance parameters making use of thousands of N-body simulations. We perform all the halo measurements in redshift space with a single sample comprised of all halos with mass $>3.2 imes 10^{13}~h^{-1}M_\odot$. For local PNG, measurements of the scale dependent bias effect from the power spectrum using sample variance cancellation provide significantly tighter constraints than measurements of the halo bispectrum. In this case measurements of the small scales add minimal additional constraining power. In contrast, the information on equilateral and orthogonal PNG is primarily accessible through the bispectrum. For these shapes, small scale measurements increase the constraining power of the halo bispectrum by up to $ imes4$, though the addition of scales beyond $k\approx 0.3 \mathrm{h/Mpc}$ improves constraints largely through reducing degeneracies between PNG and the other parameters. These degeneracies are even more powerfully mitigated through combining power spectrum and bispectrum measurements. However even with combined measurements and small scale information, equilateral non-Gaussianity remains highly degenerate with $\sigma_8$ and our bias model.

Motivation & Objective

• To assess the information content of halo power spectrum and bispectrum on small scales (k ≤ 0.5 h/Mpc) for constraining primordial non-Gaussianity (PNG).
• To investigate whether small-scale measurements break degeneracies between PNG and cosmological or nuisance parameters such as σ8 and bias.
• To evaluate the relative constraining power of the halo power spectrum versus the halo bispectrum across four PNG shapes: local, equilateral, orthogonal-LSS, and orthogonal-CMB.
• To examine the impact of sample variance cancellation, shot noise, and bias modeling on PNG inference using thousands of N-body simulations.

Proposed method

• The analysis uses the Quijote-PNG simulation suite, which includes 20,000 N-body simulations with varying cosmological and PNG parameters.
• Halo power spectrum monopole, quadrupole, and cross-spectrum with matter are measured in redshift space using a single halo sample (M > 3.2 × 10¹³ h⁻¹ M⊙).
• The halo bispectrum monopole is measured in redshift space, with careful treatment of shot noise using Gaussian process smoothing and a new Fisher information estimator.
• Fisher matrix forecasts are computed using the full covariance matrix, including super-sample covariance, to assess parameter constraints.
• Degeneracy breaking is quantified by comparing constraints with and without small-scale data (k > 0.3 h/Mpc), and by combining power spectrum and bispectrum measurements.
• Bias modeling is tested via alternative parameterizations (e.g., replacing mass cut-off with linear bias b₁) and by fitting without bias parameters to assess sensitivity to bias uncertainty.

Experimental results

Research questions

• RQ1 How does including small-scale halo power spectrum and bispectrum measurements (up to k = 0.5 h/Mpc) improve constraints on primordial non-Gaussianity?
• RQ2 For which PNG shapes—local, equilateral, orthogonal—is the bispectrum more informative than the power spectrum, and why?
• RQ3 To what extent do small-scale measurements break degeneracies between PNG and cosmological parameters like σ8 or bias parameters?
• RQ4 How does shot noise in the halo bispectrum affect Fisher matrix forecasts, and what methods mitigate this bias?
• RQ5 How robust are PNG constraints to uncertainties in the halo bias model, especially when higher-order bias terms are neglected?

Key findings

• For local PNG, power spectrum measurements with sample variance cancellation yield significantly tighter constraints than the halo bispectrum, and small-scale data add minimal additional constraining power.
• For equilateral and orthogonal PNG, small-scale halo bispectrum measurements increase constraining power by up to a factor of four, primarily by reducing degeneracies with σ8 and bias parameters.
• The addition of scales beyond k ≈ 0.3 h/Mpc improves constraints mainly by mitigating degeneracies rather than adding new information.
• The halo bispectrum's shot noise dominates on small scales, making accurate derivative estimation challenging; two mitigation methods—Gaussian process smoothing and a new Fisher estimator—were essential to avoid biased forecasts.
• Combining power spectrum and bispectrum measurements significantly improves constraints, but equilateral PNG remains highly degenerate with σ8 and the bias model, even with small-scale data.
• Constraints are conservative estimates, as marginalizing over realistic bias uncertainties—especially tidal biases—would likely degrade them further, suggesting the results represent a 'best-case' scenario.