Programme
Programme
Introduction to inflation and primordial quantum fluctuations
We will review the basic mechanism of inflation and the generation of perturbations from quantum fluctuations. The emphasis will be on simple examples which can be fully worked out, leading up to the computation of two- and higher-point functions. If time permits, we will discuss soft theorems for cosmological correlators.
Introduction to inflation and primordial quantum fluctuations (cont.)
Cosmological perturbation theory and cosmological collider physics
We review cosmological perturbation theory, namely how inflationary fluctuations are generated and converted to curvature perturbation. Non-linear perturbations, i.e., non-Gaussianities will be emphasized, with a review of models generating large non-Gaussianities. After that, we will introduce cosmological collider physics – how to probe the particle content during inflation, and how to relate cosmological observations to particle physics models.
Cosmological perturbation theory and cosmological collider physics (cont.)
(for invited speakers and PIs among the participants)
Analytical approaches to cosmological correlators
This lecture will introduce several analytical strategies developed in recent years to understand and compute cosmological correlators, with a focus on their underlying analytical structure and application to cosmological collider physics. We will first review the path-integral approach and diagrammatic expansions of cosmological correlators, and then discuss a few general-purpose techniques that bypass direct Feynman integration, including the partial Mellin-Barnes representation, the differential equation method, and family-tree decomposition.
Analytical approaches to cosmological correlators (cont.)
TBA
TBA
(for invited speakers and PIs among the participants)
Observing Primordial Non-Gaussianity with Cosmological Surveys
This lecture will connect inflationary theory to observational data, focusing on the latest techniques for extracting primordial non-Gaussianity signatures in the CMB and Large-Scale Structure (LSS). I will first discuss the challenges and practicalities of constraining such signals with the CMB, and briefly present the state-of-the-art bounds from Planck. Though the CMB is a strong probe of non-Gaussianity, it’s constraining power will soon be surpassed by LSS, which requires different techniques to model. I will introduce the Effective Field Theory of Large Scale Structure (EFT) as a rigorous framework for modeling non-linear effects in the late-time universe, both from conventional gravitational evolution and primordial particle interactions. Finally, I will summarize the current state-of-the-field and important challenges for the next generation of surveys.
Observing Primordial Non-Gaussianity with Cosmological Surveys (Cont.)
Conformal Symmetry and Spin in Cosmology
Inflationary correlators inherit the symmetry structure of de Sitter space, which acts as a three-dimensional conformal symmetry on spatial slices. I will discuss how conformal symmetry constrains cosmological correlators, including those involving fields with spin. In particular, I will explain how spinning correlators can be generated from scalar ones using symmetry-preserving differential operators. These operators provide a systematic framework for constructing the allowed tensor structures and simplifying computations.
Conformal Symmetry and Spin in Cosmology (cont.)
(for invited speakers and PIs among the participants)
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