One of the most outstanding questions in modern cosmology concerns the physical
processes governing the primordial universe and the origin of cosmic structure.
These primordial signals appear in a variety of cosmic large-scale structure probes,
e.g., in the higher-order statistics of the density field and as a scale-dependent factor
in the two-point correlations of the galaxy field. The detection and measurement of
such a non-Gaussian primordial signal would generate insights into the shape of the
potential of the inflaton field, the hypothetical particle driving cosmic inflation. In the
coming years, the next generation of galaxy surveys will commence operation, with
the scientific goal of constraining the nonlinearity parameter fnl to the uncertainty
required to identify viable inflationary models. However, achieving this goal requires
novel statistical data analysis techniques to correctly account for stochastic and
systematic uncertainties when measuring these subtle signals from observations.
In this licentiate thesis, I present a new approach to measuring primordial non-
Gaussianity in galaxy redshift surveys, and demonstrate the proof of concept. Stateof-
the-art approaches use only a limited set of summary statistics of the density
field and cannot account for the full information content of the three-dimensional
cosmic structure. To address this problem, I propose a method based on the forward
modelling of the initial density field in a Bayesian hierarchical framework. The presented
method performs a full-scale Bayesian uncertainty quantification of the posterior
distribution of fnl using a Hamiltonian Markov Chain Monte Carlo approach.
The method accounts for the gravitational formation of the three-dimensional cosmic
structure and thus utilizes the full information content of the three-dimensional
dark matter density and velocity field available in the data to constrain primordial
non-Gaussianity. In this fashion, the method naturally and fully self-consistently
accounts for all stochastic uncertainties and systematic e
