Dark Screening of the Cosmic Microwave Background with Hidden-Sector Particles and New Dynamical Observables in First Order Phase Transitions

This thesis focuses on two research directions within the field of Cosmology. It comprises the main results of my work as a PhD student. Part~\ref{PartI} introduces new observables of false vacuum decay derived from real-time numerical simulations. Part~\ref{PartII} describes a new method to search for hidden-sector particles using information from Cosmic Microwave Background (CMB) and Large Scale Structure (LSS) data. The first part studies metastable `false' vacuum decay in relativistic first order phase transitions. It is a phenomenon with broad implications for Cosmology and is ubiquitous in theories beyond the Standard Model. Describing the dynamics of a phase transition out of a false vacuum via the nucleation of bubbles is essential for understanding vacuum decay and the full spectrum of observables. We study vacuum decay by numerically evolving stochastic ensembles of field theories in 1+1 dimensions from an initially metastable state. First, we demonstrate that bubble nucleation sites cluster by measuring correlation functions in simulations. Next, we show that bubbles form with a Gaussian spread of centre-of-mass velocities for a field with an initial thermal spectrum. Finally, we show that nucleation events are preceded by oscillons - long-lived, time-dependent, pseudo-stable field configurations. We provide theoretical tools to model and generalize our findings. In the second part, we introduce a new type of secondary CMB anisotropy: the patchy screening induced by resonant conversion of CMB photons into dark-sector massive scalar (axions) and vector (dark photons) bosons as they cross non-linear LSS. In two of the simplest low-energy extensions to the SM, CMB photons can resonantly convert into either dark photons or axions when their local plasma frequency matches the mass of the hidden sector particle. For the axion, the resonance also requires the presence of an ambient magnetic field. After the epoch of reionization, resonant conversion occurs in dark matter halos if the hidden-sector particles have masses in the range $10^{-13} {\rm \; eV} \lesssim m_{{\rm A^{\prime}}} \lesssim 10^{-11} {\rm \; eV}$. This phenomenon leads to new CMB anisotropies correlated with LSS, which we refer to as dark screening, in analogy with anisotropies from Thomson screening. Each process has a unique frequency dependence, distinguishing both from the blackbody CMB. In this thesis, we use a halo model-based approach to predict the imprint of dark screening on