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. State-of-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 effects associated with selection effects, galaxy biasing, and survey geometries. Notably, multiple probes of primordial non-Gaussianity are jointly incorporated: the 3-point correlation, mass distributions of galaxies, and the scale-dependent bias effect, where this final effect is included into a novel bias model I presented in this work. I apply my method to mock data based on the SDSS-III/BOSS survey, outline tests, and present preliminary results. In addition, I present a variety of scientifically valuable data products, e.g., density field reconstructions and novel maps of primordial curvature fluctuations. Finally, future work is discussed, involving different ways of how to extend the model and additional test data sets on which to apply the method.