Perturbative Likelihoods for Large-Scale Structure of the Universe

TL;DR

This paper develops a formalism to derive likelihood functions for the large-scale structure of the universe directly from perturbation theory, enabling consistent and accurate statistical analysis of cosmological data.

Contribution

It introduces a first-principles perturbative likelihood framework that automatically incorporates PT kernels and covariances, improving modeling accuracy.

Findings

Likelihoods expressed in terms of power spectrum and bispectrum

Automatic specification of PT kernels and covariances

Likelihoods consistent with perturbation theory at chosen order

Abstract

This work presents a formalism for deriving likelihoods of the cosmological density field directly from first principles within Perturbation Theory (PT). By assuming a perturbative expansion around the Gaussian initial density field and additional stochastic components, we analytically compute two forms of the likelihood. Full marginalization over all underlying fields yields the likelihood of the observed density field, expressed in terms of its summary statistics (such as the power spectrum and bispectrum), which are naturally given by the formalism, and conditioned on model parameters. Marginalizing only over the stochastic fields results in the field-level likelihood. A key strength of this method is its ability to automatically specify the precise combinations of initial field covariances and PT expansion kernels required at each perturbative order (e.g., tree-level power spectrum and bispectrum, and the 1-loop power spectrum). This guarantees that the resulting likelihoods are fully consistent with PT at the chosen order of accuracy, avoiding ad-hoc choices in constructing the statistical model.