Abstract
Inflation is the prevailing paradigm for the early universe, wherein quantum fluctuations initiate the formation of cosmic structures. Due to the extraordinarily high energy scales inherent to inflation, it naturally functions as a cosmological collider to probe physics at otherwise inaccessible energy regimes, and those information are encoded in cosmological correlation functions. In this thesis, we first review recent progress in various analytical methods for understanding and solving cosmological collider signals. We then demonstrate that the evolution of interacting massive particles in the de Sitter bulk can be understood, at leading order, as a series of resonant decay and production events. This insight enables us to classify cosmological collider signals into local and nonlocal categories, each with distinct physical origins. Consequently, we derive a cutting rule for efficiently extracting these signals analytically. Our cutting rule offers a practical approach for extracting cosmological collider signals in model building.
In the latter part of this thesis, we investigate the evolution of correlation functions in the late universe by examining scalar-induced tensor fluctuations. We identify several previously overlooked one-loop-order contributions to secondary gravitational waves induced at nonlinear order in cosmological perturbations. We propose a consistent perturbative expansion up to the third order in cosmological perturbations during both matterand radiation-dominated eras, incorporating higher-order interactions not considered in prior studies. We demonstrate that these new contributions can play a crucial role in gravitational wave measurements.