Cosmological inference from Bayesian forward modelling of deep galaxy redshift surveys

TL;DR

This paper introduces a Bayesian framework leveraging an Alcock-Paczyński test to extract cosmological parameters from galaxy redshift surveys, using Lagrangian perturbation theory to model the density field and achieving robustness against galaxy bias.

Contribution

It presents a novel AP test that constrains the cosmological redshift transformation without relying on full statistical modeling, enhancing information extraction from galaxy surveys.

Findings

The method accurately recovers cosmological parameters from mock data.

Robustness to galaxy bias and model misspecification demonstrated.

Extracts more information than traditional correlation-based approaches.

Abstract

We present a large-scale Bayesian inference framework to constrain cosmological parameters using galaxy redshift surveys, via an application of the Alcock-Paczy\'nski (AP) test. Our physical model of the non-linearly evolved density field, as probed by galaxy surveys, employs Lagrangian perturbation theory (LPT) to connect Gaussian initial conditions to the final density field, followed by a coordinate transformation to obtain the redshift space representation for comparison with data. We generate realizations of primordial and present-day matter fluctuations given a set of observations. This hierarchical approach encodes a novel AP test, extracting several orders of magnitude more information from the cosmological expansion compared to classical approaches, to infer cosmological parameters and jointly reconstruct the underlying 3D dark matter density field. The novelty of this AP test lies in constraining the comoving-redshift transformation to infer the appropriate cosmology which yields isotropic correlations of the galaxy density field, with the underlying assumption relying purely on the cosmological principle. Such an AP test does not rely explicitly on modelling the full statistics of the field. We verify in depth via simulations that this renders our test robust to model misspecification. This leads to another crucial advantage, namely that the cosmological parameters exhibit extremely weak dependence on the currently unresolved phenomenon of galaxy bias, thereby circumventing a potentially key limitation. This is consequently among the first methods to extract a large fraction of information from statistics other than that of direct density contrast correlations, without being sensitive to the amplitude of density fluctuations. We perform several statistical efficiency and consistency tests on a mock galaxy catalogue, using the SDSS-III survey as template.