A rigorous EFT-based forward model for large-scale structure

Abstract

Conventional approaches to cosmology inference from galaxy redshift surveys are based on n-point functions, which are under rigorous perturbative control on sufficiently large scales. Here, we present an alternative approach, which employs a likelihood at the level of the galaxy density field. By integrating out small-scale modes based on effective-field theory arguments, we prove that this likelihood is under perturbative control if certain specific conditions are met. We further show that the information captured by this likelihood is equivalent to the combination of the next-to-leading order galaxy power spectrum, leadingorder bispectrum, and BAO reconstruction. Combined with MCMC sampling and MAP optimization techniques, our results allow for fully Bayesian cosmology inference from largescale structure that is under perturbative control. We illustrate this via a first demonstration of unbiased cosmology inference from nonlinear large-scale structure using this likelihood. In particular, we show unbiased estimates of the power spectrum normalization σ 8 from a catalog of simulated dark matter halos, where nonlinear information is crucial in breaking the b 1 − σ 8 degeneracy.

The EFT likelihood for large-scale structure

“…The precise meaning of Gaussian stochasticities in this paper is that there is no noise in the bias coefficients, and the difference between data and theoretical prediction for the galaxy field is distributed as a Gaussian. In Section 4.1 we consider the case where only the noise in the tracer auto two-point function is non-vanishing (and our result matches that of [1] in this limit). In Section 4.2 we include the cross stochasticity between matter and tracer, and we show how the likelihood now gains some additional terms that were not considered in [1].…”

“…In Section 4.1 we consider the case where only the noise in the tracer auto two-point function is non-vanishing (and our result matches that of [1] in this limit). In Section 4.2 we include the cross stochasticity between matter and tracer, and we show how the likelihood now gains some additional terms that were not considered in [1].…”

“…• the formalism used in this work makes the inclusion of primordial non-Gaussianity straightforward. We show that in the limit of Gaussian stochasticities and only the noise in the auto correlation function of tracers being non-vanishing, the presence of PNG does not affect the form of the conditional likelihood, which is still given by the result derived in [1]. PNG then only enters through the non-Gaussian prior on δ in , and through the new terms in the deterministic bias expansion induced by PNG, most famously the "scale-dependent bias" ∼ ∇ −2 δ in case of local-type PNG.…”

“…P[δ|δ in ] is instead given by the forward model for matter and gravity: for a deterministic evolution, this is simply a Dirac delta functional δ (∞) (δ − δ fwd [δ in ]), where δ fwd [δ in ] is the forward model for matter (such as N-body simulations, for example). 1 The goal evolution of the matter field are "absorbed" into the matter likelihood, and they disappear from P[δ g |δ] once we divide the joint likelihood by P[δ]; 2…”

“…Section 4 contains a first computation of the likelihood where, using a terminology that reflects the assumptions of [1], we assume "Gaussian stochasticities". The precise meaning of Gaussian stochasticities in this paper is that there is no noise in the bias coefficients, and the difference between data and theoretical prediction for the galaxy field is distributed as a Gaussian.…”