The EFT Likelihood for Large-Scale Structure

Abstract

We derive, using functional methods and the bias expansion, the conditional likelihood for observing a specific tracer field given an underlying matter field. This likelihood is necessary for Bayesian-inference methods. If we neglect all stochastic terms apart from the ones appearing in the auto two-point function of tracers, we recover the result of Schmidt et al., 2018. We then rigorously derive the corrections to this result, such as those coming from a non-Gaussian stochasticity (which include the stochastic corrections to the tracer bispectrum) and higher-derivative terms. We discuss how these corrections can affect current applications of Bayesian inference. We comment on possible extensions to our result, with a particular eye towards primordial non-Gaussianity. This work puts on solid theoretical grounds the EFT-based approach to Bayesian forward modeling.

arXiv comment53 pages (36+17), 4 tables. v2: matches JCAP version. Added section to compare with Schmidt et al., 2018; added plot to show relative importance of different contributions to log-likelihood

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Cited by in corpus (26)

• Galaxy bias from forward models: linear and second-order bias of IllustrisTNG galaxies
• An $n$-th order Lagrangian Forward Model for Large-Scale Structure
• How much information can be extracted from galaxy clustering at the field level?
• ENCORE: An $\mathcal{O}(N_{\mathrm{g}}^2)$ Estimator for Galaxy $N$-Point Correlation Functions
• Unbiased Cosmology Inference from Biased Tracers using the EFT Likelihood
• Consistency tests of field level inference with the EFT likelihood
• Machine Learning for Observational Cosmology
• Sigma-Eight at the Percent Level: The EFT Likelihood in Real Space
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• Cosmology inference at the field level from biased tracers in redshift-space
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• Straightening the Ruler: Field-Level Inference of the BAO Scale with LEFTfield
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• The Manticore Project II: Bayesian digital twins of cosmic structure across the SDSS and BOSS volumes
• On the Connection between Field-Level Inference and $n$-point Correlation Functions