Causality and unitarity in the early universe

Abstract

The early universe, with its high energy scales, provides a unique opportunity to explore new physics. Insights into this are encoded in the correlation functions of primordial perturbations, observable through the CMB and LSS anisotropies. To maximize these insights, it is essential to adapt tools from scattering amplitudes and open quantum systems to cosmology and to understand how fundamental principles shape cosmological correlators. This thesis examines some of the outcomes of this effort. The first three chapters are an introduction to theoretical cosmology with standard material on scattering amplitudes and the wavefunction of the universe. The following two chapters address how causality affects cosmological correlators. Chapter 4 applies Landau analysis to cosmological correlators, focusing on massless fields in flat space. From this, UV/IR sum rules are derived and validated with a tree-level exchange example. Chapter 5 develops causality-based cutting rules that break loop integrands into tree-level discontinuities, streamlining cosmological computations. These rules lead to the cosmological KLN theorem, ensuring the absence of certain singularities under general conditions. The remaining chapters focus on unitarity. Chapter 6 introduces an open effective theory of inflation in the decoupling limit, constructed using non-linearly realized symmetries. It explores two-point functions, and bispectra in Minkowski and de Sitter spacetimes, and the matching to a concrete UV model. Chapter 7 analyses electromagnetism in a dielec- tric as an open system, highlighting gauge symmetry and the role of dissipation in current and noise conservation. This chapter includes a discussion of the extension of this formalism to gravity. Chapter 8 presents positivity bounds from a new de Sitter S-matrix. These bounds are used to impose constraints on templates for the primordial bispectrum and trispectrum, providing valuable priors for future surveys. Chapter 9 is the conclusion of this thesis.