The studies presented in this thesis describe applications of quantum field theory in a time dependent background. Two distinct problems are addressed in the framework of inflationary cosmology.
The strict predictions of inflation are mostly in agreement with the Cosmic Microwave Background observations. In the recent years, large scale anomalies in the data motivated a series of analyses leading to a detection of broken statistical isotropy. Assuming that this effect is sourced by early time cosmology, I discuss the phenomenology of inflationary models extended to anisotropic backgrounds. Due to lack of rotational invariance, these models generically involve a system of coupled quantum fields. This leads to a tensor-scalar correlation function, which is a characteristic signature of these models.
Another open question in cosmology involves the transition from inflation to the Hot Big Bang cosmology. In the presence of supersymmetric flat directions, the formation of the thermal radiation may undergo a dramatic delay, provided that these directions decay only perturbatively. In the scope of a toy model and a realistic example, both involving two flat directions, I discuss the nonperturbative decay that rapidly depletes the flat directions. If realized, this process can dramatically affect the previous assumptions on the thermalization scale. Due to the vast number of degrees of freedom, this problem generically involves coupled quantum fields. The decay of the flat directions gets contributions from both the diagonal (nonadiabatic evolution of frequency eigenvalues) and nondiagonal (nonadiabatic evolution of frequency eigenstates) effects. An additional characteristic effect of coupled quantization is the rotation of light eigenstates to heavy ones, which do not get produced in a diagonal system.