The cosmological bootstrap and the analytic wavefunction

Abstract

In the past few decades there have been an overabundance of models describing inflation, a period where the universe expands exponentially quickly. This led to the rise of the cosmological bootstrap, which aims at constraining cosmological observables in a model independent way. This is achieved by directly imposing physical principles such as unitarity, locality, symmetry, and analyticity on cosmological correlators. In this thesis we explore the consequences of two such principles: unitarity and analyticity. We show that unitarity implies a set of consistency relations among wavefunction coefficients in perturbation theory, and these relations can be generalized to fields with any mass and integer spin. Unitarity, alongside locality and scale invariance, also implies the vanishing of four-point parity odd correlators at tree level, and we show this is not true at loop level. Analyticity in the S-matrix is linked to causality and serves as the backbone for the S-matrix bootstrap, which provides non-perturbative constraints for scattering. We show that analyticity in the wavefunction is also linked to causality. We study the analytic structure of the wavefunction in detail and demonstrate the relation between singularities in amplitudes and a subset of singularities in the wavefunction. Finally, we write down the dispersion relations of the wavefunction, which serves as a first step towards a non-perturbative bootstrap in cosmology.