Master's Thesis in Theoretical Physics - Universiteit Utrecht

solution to the homogeneity puzzle. Suppose we have some initial energy density of cosmicrelics ρ relics . During inflation, the size of the universe increases by an enormous factor(the scale factor increases by a factor e N , which is huge). Therefore, any preexisting energydensity of cosmic relics is diluted to practically nothing and we will never observe cosmicrelics such as magnetic monopoles.3.4 Inflationary modelsInflation is basically an epoch during which the scale factor accelerates, thus the universeundergoes an accelerated expansion. Formally, inflation occurs whenSince äa = Ḣ + H2 , this also meansä > 0. (3.11)ɛ = − Ḣ < 1. (3.12)H2 From Eq. (2.8) we see that we need to haveρ + 3p < 0. (3.13)This means that we need some special field with p < − 1 3ρ, i.e. negative pressure. This ispossible within certain particle physics models. An essential ingredient is a scalar field.As we know from the Standard Model, in scalar field models a phenomenon known as theHiggs mechanism can occur. The potential of a scalar field φ can be such that there are twominima and the scalar field is initially in the minimum with the lowest value (at φ = 0).However, as time increases and the temperature drops, the second minimum at φ ≠ 0. cantake a lower value than the initial minimum. We then say that the scalar field is in thefalse vacuum state and it wants to be in the true vacuum state. A phase transition will takeplace, in which the scalar field moves from the initial symmetric vacuum phase at φ = 0 tothe non-symmetric vacuum phase at φ ≠ 0. This is a process known as spontaneous symmetrybreaking. Going back to the statement that we need negative pressure for successfulinflation, first realize that negative pressure is not that unusual if you think of it as anattractive force. Basically, the scalar field is pulled out of its false vacuum state into thetrue vacuum, thus the scalar field experiences negative pressure.Alan Guth used precisely the mechanism of spontaneous symmetry in his original article[3] on "old" inflation. He considers a first order phase transition, which means that thereis a potential barrier between the false vacuum and the true vacuum. The idea is that thescalar field wants to move to the true vacuum, but it cannot because of the barrier, and itis trapped in the false vacuum state with some high temperature. The true vacuum willbecome lower and lower as the temperature drops, until finally at some low temperaturethe scalar field will finally move to the true vacuum. The latent heat is released and thisgenerates a huge entropy production which solves the flatness and horizon puzzles. Theflaw in this original model is that the bubbles of the true vacuum phase that are formedcannot overtake the rapid expansion of the universe. In other words, the universe expandsfaster that the bubbles grow, so the bubbles never coalesce and the universe never reachesthe true vacuum state. Thus, inflation never ends, a problem known as the graceful exitproblem.Linde[6] and Albrecht and Steinhardt[7] proposed a new inflationary model, not surprisinglyknown as new inflation. In this scenario the universe will undergo a second orderphase transition or a crossover, such that no bubbles are formed and the universe will as