Exploring Relativistic and Parity-Odd Signatures in Large-Scale Structure

Galaxies trace the cosmic web of clusters, filaments and voids and their large-scale distribution provides one of our richest probes of structure formation. In practice, however, we observe galaxies in redshift space, not their true distances, so their apparent positions are distorted by their motions. This gives rise to the familiar redshift-space distortions. On the largest observable scales, further relativistic effects also begin to matter. These include effects local to the source, such as Doppler, while others arise during the propagation of light to the observer. These corrections can introduce line-of-sight asymmetries and more subtle anisotropic distortions beyond the standard picture. In this talk, I will review my work on relativistic effects in large-scale structure, focusing in particular on their signatures in higher-order clustering statistics. These observables offer new ways to search for asymmetries in the large-scale distribution of galaxies, opening a window onto relativistic effects on cosmological scales and possible traces of new physics from the early Universe.  As upcoming surveys push to ultra-large scales with unprecedented precision, understanding these effects is becoming increasingly timely.