The analytic cosmological correlator

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The goal of the project is to make predictions for cosmological correlators generated during cosmic inflation in the first fraction of a second of the big bang. Cosmological correlators provide the initial conditions for the subsequent evolution of all constituents of our universe, including for example photons, neutrinos, baryonic matter and dark matter. Hence, these predictions can be tested in current and upcoming cosmological surveys of the cosmic microwave background and large scale structures (e.g. galaxy and weak-lensing surveys, intensity mapping, etc). So far only the two point correlation function has been detected and one of the main science goals of a large number of international experiments is to detect higher point functions, collectively denoted as non-Gaussianity.This project aims at developing a new methodology to compute non-Gaussianity that is model-agnostic and relies on imposing constraints from fundamental principles of physics. In particular, the relevant principles are symmetries, the conservation of probability (unitarity), the absence of action at distance (locality) and the consistent separation between cause and effect (causality). The constraints imposed by the conservation of probability have been much better understood in recent years, but further progress is still required. One goal of this project is to formulate these unitarity constraints without relying on perturbation theory. This will be essential to extract information from possible UV-completions, which are usually not known in detail.The constraints imposed by locality, namely the absence of interaction at distance, will be derived in the form of precise bounds on the growth of correlators for complex kinematics. The goal is to establish these bounds in full generality for large classes of theories, e.g. for particles of any mass and any spin on an approximately de Sitter spacetime. The constraints from causality will dictate the analytic structure of correlators for complex kinematics, in a way similar to what happens for scattering amplitudes in flat spacetime. No such constraints are known to date.Finally, in the last part of this PhD project, the above ingredients will be combined to derive bounds that low-energy effective field theory have to satisfy if they are to admit a consistent, unitarity, local and causal UV-completions. These so-called positivity bounds are known in flat space but not in cosmological spacetime. Here they will be derived around an inflationary spacetime and for a dark energy dominated universe (quasi de Sitter).