Towards optimal extraction of cosmological information from nonlinear data

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 [1]. 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:1909.04022v1 [astro-ph.CO] 9 Sep 2019 1 Even if we use an N-body simulation to forward-model the matter field, the evolution is never deterministic (due to the fact that, by construction, N-body simulations still integrate out all sub-grid modes), so the assumption of having a Dirac delta functional is not technically correct. We will see below that this is naturally taken into account by the approach used in this paper. of this paper is to compute P[δ g |δ] using the effective field theory of biased tracers.Let us outline our general strategy to compute P[δ g |δ]. First, we can use the properties of conditional probabilities to express this as the ratio of the joint probability P[δ g , δ] and the probability P[δ] for the matter field itself. How do we compute these two quantities? We know how to compute correlation functions of δ g and δ using the effective field theory of large-scale structure (EFT of LSS)/bias expansion. More generally, we know how to compute the full generating functionals Z[J] and Z[J g , J], the first for the correlation functions of δ alone, and the second for those of δ g and δ together. The generating functional for matter correlation functions in the EFT of LSS was discussed for the first time (to the authors' knowledge) in [13]: here we extend it for the first time to include also biased tracers.Once we have the two generating functionals Z[J] and Z[J g , J], an expression for P[δ] and P[δ g , δ] can be easily obtained via the inverse functional Fourier transform. This allows us to cast the problem of computing these probability density functionals (henceforth "likelihoods", for simplicity) using methods of functional integration commonly employed in quantum field theory. As we will see below, this method successfully recovers the result of [1], where the authors computed P[δ g |δ] using the assumption that the noise field ε g (that enters in the linear bias expansion of δ g as δ g = b 1 δ + ε g ) is a Gaussian-distributed variable.On top of this, the approach developed here gives a simple and rigorous way of computing the corrections to this result which come, for example, from the wrong assumption of having Gauss...

Section: Adding P εGεmmentioning

confidence: 99%

The EFT likelihood for large-scale structure

Cabass

Schmidt

2020

“…This approach offers the advantage of a much more straightforward incorporation of systematic effects. Starting from early attempts based on galaxy peculiar velocities [4,5], this approach is being pursued increasingly actively [6][7][8][9][10][11][12][13][14][15][16]. The forward model for matter, together with the perturbative bias expansion, provides us with a "mean tracer field" in a certain sense.…”

Section: Introductionmentioning

confidence: 99%

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

Schmidt

Elsner

Jasche

et al. 2019

197

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.

“…Here we summarize the optimization technique and standardize notation. For a complete description, see [12,14,15].…”

Section: Introductionmentioning

confidence: 99%

Efficient optimal reconstruction of linear fields and band-powers from cosmological data

Horowitz

Seljak

Aslanyan

2019

We present an efficient implementation of Wiener filtering of real-space linear field and optimal quadratic estimator of its power spectrum. By recasting the reconstruction into an optimization problem, we provide a flexible framework that can be used on a variety of cosmological fields. We present results for a variety of test cases, using simulated examples of projected density fields, projected shear maps from galaxy lensing, and observed Cosmic Microwave Background (CMB) temperature anisotropies, with a wide range of map incompleteness and variable noise. For smaller cases where direct numerical inversion is possible, we show that the maximum a posteriori solution matches that created by direct Wiener Filtering at a fraction of the overall computation cost. This technique allows for accurate map and power spectrum reconstruction even with complex masks and nontrivial noise properties.