Theoretical Study of Cosmological Correlators and Large-Scale Structure

Abstract

Modern cosmology seeks to reconstruct the evolutionary history of the Universe, from quantum fluctuations generated during inflation to the late-time formation of Large Scale Structure (LSS). The statistical information encoded in cosmological correlators provides a powerful probe of both primordial interactions and the subsequent non-linear evolution of matter. This thesis develops analytical approaches based on symmetries, unitarity, and bootstrap principles to overcome the computational challenges associated with cosmological observables. In the early-universe context, we employ cosmological dressing rules to uplift flat-space unitarity cuts into exact discontinuity relations for Euclidean AdS/de Sitter observables, providing a diagrammatic origin for cosmological cutting rules and verifying them at tree and one-loop levels. We also study inflationary non-Gaussianities in \(\alpha\)-vacua by computing four-point scalar correlators and demonstrating their consistency with conformal Ward identities. We then turn to the late-time, non-linear regime of LSS within the Effective Field Theory of Large Scale Structure (EFTofLSS), where the finite response time of short-scale modes induces temporal non-locality or memory effects. We show that for observables breaking rotational symmetry from \(SO(3)\) to \(SO(2)\), relevant for line-of-sight probes such as the Lyman-\(\alpha\) forest, time non-locality appears already at third order in perturbation theory, rather than the previously expected fifth order. Finally, we develop the bootstrap approach based on Extended Galilean Invariance (EGI) to fifth order in both Eulerian and Lagrangian spaces, introducing a novel procedure to remove spurious poles and fully reconstruct the time-non-local bias expansion, while identifying tracer-independent ratios of bias coefficients that provide clean probes of the underlying cosmology.