Quantum and thermal effects on inflation and neutrino dynamics in the early Universe

In this thesis, we investigate quantum and thermal effects on inflation and neutrino dynamics in the early Universe. In the first part, we study the dynamics of interacting scalar fields from first principles of nonequilibrium quantum field theory, to explore the feasibility of warm cosmic inflation models. Warm inflation is an alternative to the standard cold paradigm, a speculative phase of exponentially accelerated expansion of the primordial Universe which explains its overall geometry, isotropy and homogeneity. Using the formalism of 2 Particle Irreducible effective actions, we establish the evolution equations that govern the nonequilibrium dynamics of the field expectation value and two-point functions, which we express in terms of Feynman diagrams. Assuming a separation of time scales between quantum processes and the time evolution of bulk properties of the system, we solve the equations of motion for the two-point functions analytically at next-to-leading order (NLO) in the loop expansion. We then use these to compute quantum and thermal corrections to the damping rate and effective potential that drive the dynamics of the field expectation value. These computations require to address formal questions in nonequilibrium field theory, such as renormalisation in a time-dependent background. They can potentially be applied to any quantum system effectively described by (pseudo)scalars, e.g. cosmic reheating or generically particle production in the early Universe. To conclude this part, we utilise our computations to prove the existence of a regime where the field expectation value undergoes an overdamped motion, as needed for warm inflation models. In the second part, we provide input for a state-of-the-art precision computation of the effective number of cosmological neutrinos Neff. The latter is a well-measured cosmological observable that is sensitive to physics beyond the Standard Model and used for fundamental parameter inference. From first principles of finite-temperature quantum field theory, we study corrections to Neff = 3 to an unprecedented level of accuracy, including for the first time NLO and NNLO quantum electrodynamical (QED) corrections. Our computations resolve a dispute in the literature on the theoretical value of Neff. Given the precision of current and future experiments, we show in the instantaneous decoupling approximation (IDA) that NLO corrections must be considered standard inputs for future Neff computations and provide the necessary analytic ingredients to implement them when dropping the IDA. Higher order QED corrections are negligible.