Cosmological inference from Bayesian forward modelling of deep galaxy
  redshift surveys
  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.
