One of the most pressing questions in modern cosmology pertains to the physical processes governing the early universe and the origins of cosmic structure. Primordial signals are manifest in various probes of the large-scale cosmic structure, such as the higher-order statistics of the density field and the scale-dependent bias effect. Detecting and measuring non-Gaussian primordial signals would shed light on the potential shape of the inflaton field, the hypothetical particle responsible for cosmic inflation. In the near future, next-generation galaxy surveys will begin operation, aiming to constrain the non-linearity parameter fNL to the degree of uncertainty necessary for identifying feasible inflationary models. Nevertheless, accomplishing this objective necessitates modern statistical data analysis tools to accurately account for stochastic and systematic uncertainties when extracting these subtle signals from observations.

In this thesis, I describe a novel approach for measuring primordial non-Gaussianity in galaxy redshift surveys that I have developed. The method is based on a Bayesian field-level inference technique, which includes the full field to constrain fNL. In this way, the method is able to go beyond current state-of-the-art methods, which employ a limited set of summary statistics, to capture the full information content of the three-dimensional cosmic structure. The method uses a physical forward model that translates any set of initial conditions to a predicted observable. The space of plausible initial conditions and cosmological parameters are sampled with the help of a Bayesian framework utilizing a Hamiltonian Monte Carlo approach. The method accounts for the gravitational formation of the three-dimensional cosmic structure, and inherently and fully self-consistently accounts for all stochastic uncertainties and systematic effects associated with selection effects, galaxy biasing, and survey geometries. The method is able to account for multiple probes of primordial non-Gaussianity, e.g. the higher-order correlation functions, galaxy mass distributions, peculiar velocity fields, and the scale-dependent bias effect. I showcase highlights of the development process, and present work in inferring primordial non-Gaussianity in galaxy survey data sets. Lastly, necessary preparation for next-generation galaxy redshift surveys is discussed.

Detecting and measuring a non-Gaussian signature of primordial origin in the density field is a major science goal of next-generation galaxy surveys. The signal will permit us to determine primordial-physics processes and constrain models of cosmic inflation. While traditional approaches use a limited set of statistical summaries of the galaxy distribution to constrain primordial non-Gaussianity, we present a field-level approach by Bayesian forward modelling the entire three-dimensional galaxy survey. Since our method includes the entire cosmic field in the analysis, it can naturally and fully self-consistently exploit all available information in the large-scale structure, to extract information on the local non-Gaussianity parameter, fnl. Examples include higher order statistics through correlation functions, peculiar velocity fields through redshift-space distortions, and scale-dependent galaxy bias. To illustrate the feasibility of field-level primordial non-Gaussianity inference, we present our approach using a first-order Lagrangian perturbation theory model, approximating structure growth at sufficiently large scales. We demonstrate the performance of our approach through various tests with self-consistent mock galaxy data emulating relevant features of the SDSS-III/BOSS-like survey, and additional tests with a Stage IV mock data set. These tests reveal that the method infers unbiased values of fnl by accurately handling survey geometries, noise, and unknown galaxy biases. We demonstrate that our method can achieve constraints of σ_fnl≈8.78 for SDSS-III/BOSS-like data, indicating potential improvements of a factor ∼2.5 over current published constraints. We perform resolution studies on scales larger than ∼16h⁻¹ Mpc showing the promise of significant constraints with next-generation surveys. Furthermore, the results demonstrate that our method can consistently marginalize all nuisance parameters of the data model. The method further provides an inference of the three-dimensional primordial density field, providing opportunities to explore additional signatures of primordial physics. This first demonstration of a field-level inference pipeline demonstrates a promising complementary path forward for analysing next-generation surveys.

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.