On priors and scale cuts in EFT-based full-shape analyses

TL;DR

The paper investigates how priors and scale cuts influence EFT-based full-shape analyses of galaxy clustering, identifying two main biases: prior-volume projection and genuine two-loop theory biases that do not vanish with better priors or larger data volumes. By contrasting West Coast (WC) and East Coast (EC) pipelines and testing on the PT Challenge and BOSS-like data, it shows that optimistic scale cuts and inconsistent stochastic modeling in WC lead to significant biases in σ₈ (up to ~5%) and modest biases in ω_cdm, whereas EC3 with multi-probe data and consistent stochastic terms keeps biases well below the statistical errors. The work demonstrates that scale cuts are a major driver of bias, and that including scale-dependent stochastic counterterms, higher-order counterterms, and multiple observables (bispectrum, hexadecapole) reduces both theory and projection biases. Practically, this supports using conservative k_max, simulation-informed priors, and comprehensive data vectors for robust cosmological inference with EFT-based full-shape analyses in current and upcoming surveys like DESI and Euclid.

Abstract

Parameter estimation from galaxy survey data from the full-shape method depends on scale cuts and priors on EFT parameters. The effects of priors, including the so-called ''prior volume'' phenomenon have been originally studied in Ivanov et al. (2019) and subsequent works. In this note, we repeat and extend these tests and also apply them to other priors used in the literature. We point out that in addition to the ''prior volume'' effect there is a more dangerous effect that is largely overlooked: a systematic bias on cosmological parameters due to overoptimistic scale cuts. Unlike the ''prior volume'' effect, this is a genuine systematic bias due to two-loop corrections that does not vanish with better priors or with larger data volumes. Our study is based on the high fidelity BOSS-like PT Challenge simulation data which offer many advantages over analyses based on synthetic data generated with fitting pipelines. We show that some analysis choices associated with the PyBird code, especially the scale cuts, significantly bias parameter recovery, overestimating $σ_8$ by over $5\%$ (equivalent to $1σ$). The bias on measured EFT parameters is even more significant. In contrast, the analysis choices associated with the CLASS-PT code lead to much smaller ($\lesssim 1\%$) shifts in cosmological parameters based on their best-fit values.

Figures (4)

• Figure 1: Posterior distributions inferred from the single snapshot of the PT challenge simulation at $z_{\rm eff}=0.61$ in the WC and EC3 models using the analytical covariance matching the BOSS survey volume 5.8 ($h^{-1}$Gpc)$^3$, and the covariance corresponding to the total simulation volume $566\,(h^{-1}\text{Gpc})^3$.
• Figure 2: Posterior distributions from the different analyses of the PT challenge simulation for the WC model ( upper left panel), the EC1 model ( upper right panel), the EC2 model ( lower left panel) and the EC3 model ( lower right panel). The results are inferred from the four BOSS-like data chunks (green), as well as from the single snapshot at $z_{\rm eff}=0.61$ with the covariance matching the BOSS survey volume (blue), and the covariance rescaled to match the full PT challenge volume 566 ($h^{-1}$Gpc)$^3$ (red). For the EC2 model, we also show the analysis with $k_{\rm max}=0.2\,h \text{Mpc}^{-1}$ and the covariance corresponding to the full simulation volume (in pink).
• Figure 3: Posterior distributions inferred from the four BOSS-like samples of the PT Challenge simulation using the BOSS data covariance estimated from the Patchy mocks ($V_{\rm BOSS}$) and the analytical Gaussian covariance corresponding to 100 times the BOSS volume ($100\times V_{\rm BOSS}$). For $100\times V_{\rm BOSS}$, only the mean values of the corresponding parameters are depicted by dashed lines.
• Figure 4: Posterior distributions inferred from the four BOSS-like samples of the PT Challenge simulation using the BOSS data covariance estimated from the Patchy mocks ($V_{\rm BOSS}$) and the analytical Gaussian covariance corresponding to 100 times the BOSS volume ($100\times V_{\rm BOSS}$). For $100\times V_{\rm BOSS}$, only the mean values of the corresponding parameters are depicted by dashed lines. For the WC and EC2 models, the $k_{\rm max}^{\rm z_1}/k_{\rm max}^{\rm z_3}=0.2/0.23\,h \text{Mpc}^{-1}$ are adopted, while for the EC3 model $k_{\rm max}=0.2\,h \text{Mpc}^{-1}$ is used for both redshift bins.