Symmetry breaking in de Sitter: a stochastic effective theory approach
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I first give some details on current experimental observations about our universe, as well as on the standard cosmological model. Then I introduce the idea of the fast expansion of the universe (namely, the inflation), discussing on the one hand experimental and theoretical problems it allows to solve and on the other, its main implementations, since it was introduced for the first time, in 70’s. A description of the so called stochastic approach (first due to Starobinsky and later described again together with Yokoyama - SY) for a scalar model follows, including the main physical results of some applications in other theories. In chapter 4 I describe in details our work. In the first part, we explore the presence of a spontaneous symmetry breaking, using the field probability distribution function (PDF) resulting from the SY Fokker-Planck equation. In contrast with the SY work, no condensate is found, both in O(1) and O(N) scalar model. In the second part, we construct an effective field theory, plotting the effective potential and the effective PDF. They confirm the result of the first part: indeed, the effective potential is strictly convex, as we can also prove analytically. In the last two chapters, further discussions follow, based on small and big field values expansions of effective potential and on our estimation for the back-reaction on the geometry.