Straightening the Ruler: Field-Level Inference of the BAO Scale with LEFTfield

TL;DR

This work develops a fully Bayesian, field-level approach to inferring the isotropic BAO scale by jointly sampling initial conditions, cosmology, and bias within an EFT-based forward model (LEFTfield). By varying the BAO scale through the parameter $\beta$ and using a Gaussian EFT likelihood, the method remains robust to model mismatch against high-resolution mock data and yields BAO constraints that are typically $30$–$50\%$ tighter than standard post-reconstruction power-spectrum analyses on the same scales. Validation tests against linear and 1LPT mock data show consistency with optimal reconstruction results in those limits, while the Eulerian bias implementation consistently reduces residual biases to $<1\%$ across scales. The results indicate that field-level BAO inference not only provides a coherent inference framework for the BAO scale but also promises enhanced precision for realistic, nonlinearly biased tracers, with potential extensions to full N-body simulations, redshift-space distortions, and joint cosmology inference via SBI.

Abstract

Current inferences of the BAO scale from galaxy clustering employ a reconstruction technique at fixed cosmology and bias parameters. Here, we present the first consistent joint Bayesian inference of the isotropic BAO scale, jointly varying the initial conditions as well as all bias coefficients, based on the EFT-based field-level forward model $\texttt{LEFTfield}$. We apply this analysis to mock data generated at a much higher cutoff, or resolution, resulting in a significant model mismatch between mock data and the model used in the inference. We demonstrate that the remaining systematic bias in the BAO scale is below 2% for all data considered and below 1% when Eulerian bias is used for inference. Furthermore, we find that the inferred error on the BAO scale is typically 30%, and up to 50%, smaller compared to that from a replication of the standard post-reconstruction power-spectrum approach, using the same scales as in the field-level inference. The improvement in BAO scale precision grows towards smaller scales (higher $k$). As a validation test, we repeat this comparison on a mock dataset that is linearly biased with respect to a 1LPT (Zel'dovich) density field, following the assumption made in standard reconstruction approaches. We find that field-level inference indeed yields the same error bar as the post-reconstruction power spectrum, which is expectd to be optimal in this case. In summary, a field-level approach to BAO not only allows for a consistent inference of the BAO scale, but promises to achieve more precise measurements on realistic, nonlinearly biased tracers as well.

Figures (15)

• Figure 1: Trace plot of the BAO scale parameter $\beta$ for Mock A and $\Lambda = 0.2 \,h\,{\rm Mpc}^{-1}$ for three independent MCMC chains, where $n$ denotes the sample index. The chain shown in green started from the true initial conditions $\hat{s}_{\rm true}$ while the other two chains started from random initial conditions. Each chain started from a different initial $\beta$ value, with all quickly converging to the same value. Dashed black line indicates the ground truth value $\beta_0$.
• Figure 2: The normalized auto-correlation function for the BAO scale parameter $\beta$ inferred from Mock A at $\Lambda = 0.2 \,h\,{\rm Mpc}^{-1}$ (upper panel). We also display the correlation length value $\tau$ together with the maximum separation $M$ between the samples considered, both of which are defined in App. \ref{['sec: apendix']}. The correlation length of $\beta$ is estimated to be $\tau \simeq 250$ samples. In the lower panel, we zoom into the first 1800 samples of the chain.
• Figure 3: Field-level BAO inference results for Mock A. The left panel shows the inferred BAO scale relative to ground truth obtained using Lagranigan bias for sampling. FreeIC are represented using circle marker and FixedIC using a square. On the right we show the 68% CL error bar on the BAO scale, $\sigma_{\rm F}(\beta)$, as a function of cutoff $\Lambda$.
• Figure 4: Field-level BAO inference results for Mock B. The left panel displays the inferred BAO scale relative to the ground truth, where the BAO scale is sampled alongside the initial conditions. The Lagrangian bias points, computed for the same values of $\Lambda$, have been slightly displaced horizontally for better visibility. On the right, we show the 68% CL error bar, $\sigma_{\rm F}(\beta)$, as a function of the cutoff $\Lambda$. The results obtained using the Lagrangian bias are depicted in blue, while those obtained using Eulerian bias are shown in orange.
• Figure 5: Parameter posteriors for the FreeIC inference in the case of Mock B. Left panel (a) represents the Eulerian bias model while the right panel (b) represents the Lagrangian bias. The dotted gray line indicates the ground truth value $\beta_0$ in each case. The inference was performed at $\Lambda = 0.18 \,h\,{\rm Mpc}^{-1}$ in both cases.