Browsing by Author "Manninen, Peter"

The first two chapters are meant as a background for the discussion to follow. In the first chapter we start by reviewing some basic tools from cosmology to handle inflation. The scalar field equation in an expanding space is derived. We also review the Friedmann-Robertson-Walker metric and the equations that follow. From then on, our focus is on inflation. We recall the slow-roll model of inflation and consider a special case that will be useful in the later analysis. We also introduce the metastable vacuum problem resulting from the measured Higgs mass. Avoiding the possible instability of the vacuum during inflation and preheating will then be the main focus of the later chapters. The second chapter reviews how to handle the differential equations that will be presented later. The equations in question will be of the form described by the Floquet theory. We start by considering these very general differential equations and their solutions, leading to the division between stable and unstable solutions that will be manifest later on in the Higgs evolution. Using the Floquet theory we can also consider more specific equations, such as the Hill equation. In particular, we focus on two special cases of the Hill equation: the Mathieu equation and the Whittaker-Hill equation. These equations and their solutions are discussed in more detail to lay the background for the later analysis. The following chapters focus on the Higgs field and its evolution during the inflationary and preheating epochs. By introducing a Higgs-inflaton coupling, our first aim is to stabilize the Higgs field during inflation, where it could be destabilized by quantum fluctuations. We see that a quartic coupling term is enough to induce an effective mass term that stabilizes the Higgs field. After this, a larger emphasis is placed on the time after inflation. We introduce a trilinear coupling term between the Higgs and inflaton fields. While stabilizing the Higgs field during inflation, the Higgs-inflaton coupling also causes resonance effects once the inflaton field starts to oscillate around its minimum. These resonance effects could lead to destabilization during the preheating epoch. We derive some basic results describing the resonance and the possible destabilization effects. Next we introduce a non-minimal Higgs-gravity coupling and investigate how it affects the Higgs field during inflation and preheating. We derive the equations of motion using canonical normalization. We review the Higgs stability during the inflationary epoch in terms of the new equations. Then, we consider the equations in the preheating epoch. With some approximations, the resulting equations that describe the Higgs field during preheating will be those discussed before, the Mathieu equation and the Whittaker-Hill equation. We give coupling parameter bounds that ensure vacuum stability using lattice simulation results.