Title: Non-equilibrium Evolution of Scalar Fields in the Early Universe

Abstract:  This dissertation studies the non-equilibrium evolution of scalar fields in the early universe. It mainly covers three aspects of the topic. The first is the evolution of multiple fields in a thermal background, where their coupling to common decay channels in the background induces effective couplings among them, similar to $K^0-\bar{K}^0$ mixing. Within this framework, we described the decay, decoherence and thermalization of axion condensates in a connected and uniform way, discussed the Chern-Simons condensate induced in the medium by a coherent axion field and its possible observation method. We also generalized the Wigner-Weisskopf Theory to a multi-particle description for field mixing in thermal background and between particles with different masses, which complements and extends Lee-Oehme-Yang's theory of meson mixng used in the study of CP vilation. This method shows the quantum beats and asymptotic bath-induced coherence of the system, which are resonantly amplified when the masses of two particle species are close, leading to potential observational consequences. In the second aspect we revisit the effective potential method for the dynamics of a initially coherent and self-interacting scalar field. Our analysis shows that due to the profuse particle production, spinodal instability and parametric amplification, the valid regime of the effective potential is narrow. We then proposed a energy-conserving framework for this dynamics, from which we learnt that particles are produced in highly entangled two-mode squeezed states and coarse-graining of the density matrix in this basis leads to decoherence of the closed quantum systems. In the third aspect we did an ab initio calculation up to one loop for the relaxational dynamics of a scalar condensate in a radiation  dominated era. A main conclusion is that a phenomenological friction term is inadequate to describe the decay in the super-Hubble regime, during which (relevant for ultralight dark matter) the condensate amplitude decays as $(mt)^{\frac{g^2}{10} t^2}$, and in the sub-Hubble regime, a local friction term always underestimates the timescale of the condensate decay as a consequence of the cosmological expansion.