Minisuperuzay modelleri: Evren-antievren çift yaratımı ve yok edilmesi

Cosmology is an ancient area of science and has reached many advancements recently due to the discoveries in quantum physics and the improvements in observational astronomy. There have been many attempts to explain the origin of the universe. The cosmological models with homogeneous scalar fields seem to be fine-tuned with the observations and therefore enabling us to build a decent mathematical model of our cosmos. Nevertheless, there are many problems we encounter in cosmology which we will discuss below. We start with a toy model with a homogeneous scalar field and try to connect with the observations. The mathematical model with the scalar field will be mostly constructed theoretically, and some analytical solutions will be presented. We will consider a simple model in cosmology but that can be extended to more difficult models as the principles are significantly the same. This thesis will discuss The No-Boundary proposal and a simple derivation of the Wheeler-DeWitt equation for our minisuperspace model. Although there is no quantum gravity theory yet, we introduce the Wheeler-DeWitt equation and develop a spinor representation of our model. Cosmological solutions will be plotted and will be studied independently. The potential will be chosen so that we will have the case of the harmonic and anti-harmonic oscillator. In the late steps of the work, the classical time will be discussed. We will also obtain a pair of creation and annihilation of the universe at the time of creation from a preferred vacuum state if one considers that our universe was CPT symmetric at the very early times of the universe. We will also discuss the entanglement entropy of the created multiverse and a general formula for the quantized spinor solutions of the Dirac-type Wheeler-DeWitt equations in a minisuperspace model.