Relativistic Signatures in the Galaxy Bispectrum

The next generation of galaxy surveys will map the large-scale distribution of matter with unprecedented statistical precision, extending observational access to scales approaching the cosmic horizon. On these ultra-large scales, relativistic effects arising from observing an evolving Universe on the past light cone become non-negligible, and must be modelled accurately to avoid systematic bias and to fully exploit the scientific potential of forthcoming data. At the same time, these scales provide enhanced sensitivity to signatures of primordial non-Gaussianity (PNG), offering a unique window onto the physics of the early Universe. This thesis investigates how relativistic light cone effects and local PNG manifest in the statistical description of large-scale structure, with particular emphasis on higherorder clustering statistics. Working at the interface of analytical modelling and statistical inference, I develop flexible, survey-adaptable frameworks that connect relativistic perturbation theory to observable quantities measured in galaxy surveys. A central focus of this work is the galaxy bispectrum, which captures mode coupling beyond the two-point function and provides information that is both complementary and inaccessible to the power spectrum alone. On large scales, the bispectrum is especially sensitive to relativistic projection effects and local-type primordial non-Gaussianity. I quantify the relativistic contributions to the bispectrum, which generate a distinctive imaginary, leading to odd multipoles that do not cancel under symmetrisation. This feature provides a clean observational signature of relativistic effects, absent in standard Newtonian analyses. Using this framework, I perform information-matrix forecasts for the local primordial non-Gaussianity parameter fNL and for parametrised amplitudes of relativistic corrections. I quantify the impact of relativistic effects on PNG inference and demonstrate that neglecting these contributions in bispectrum analyses can lead to significant biases, with shifts exceeding 1.5σ(fNL). Conversely, I show that joint analyses can robustly disentangle relativistic and primordial contributions, with relativistic detections largely insensitive to uncertainty in fNL. Motivated by these results, I then investigate strategies to enhance the detectability of relativistic signals. In particular, I explore multi-tracer and sample-split approaches in which galaxy catalogues are divided into bright and faint sub-samples. By combining auto- and cross-bispectra, this method suppresses cosmic variance and significantly boosts iv sensitivity to relativistic contributions. Applying this framework to survey specifications representative of current and forthcoming experiments, I demonstrate that the relativistic Doppler bispectrum is accessible in stage IV galaxy surveys, even at low redshift where cosmic variance is known to be problematic. For a DESI-like bright-galaxy sample, the relativistic Doppler contribution to the auto-bispectrum yields a signal-to-noise ratio (SNR) just below the conventional detection threshold, while an optimal bright-faint split increases this by nearly an order of magnitude, establishing the Doppler bispectrum as a measurable signal in existing data. Overall, this thesis establishes the galaxy bispectrum as a powerful probe of horizonscale physics. By demonstrating both the detectability of relativistic effects and their importance for unbiased local PNG constraints, this work highlights the necessity of relativistic modelling in precision cosmology and contributes to the theoretical foundations required to interpret the next era of large-scale structure observations.