Thesis Outline. In this chapter, we have given an overview of the inflation theory, the problems that solve, and how the perturbations are generated. To explain it, we have developed the mechanism of gravitational particle creation for scalar fields. At the end of the section we have introduced the standard model ▇▇▇▇▇ field and its running, which combined with its quantum fluctuations during inflation, it leads us to the problem of the stability of the electroweak vacuum. The rest of the thesis is going to be structured as follows: • In chapter 2, we consider the effect of the ▇▇▇▇▇▇▇-▇▇▇▇▇▇▇ radiation on the inflaton in the situation where it is coupled to a large number of spectator fields. We argue that this will lead to two significant effects - a thermal contri- bution to the potential and a gradual change in parameters in the Lagrangian, which results from thermodynamic and energy conservation arguments. We present a scenario of hilltop inflation, where the field starts trapped at the origin, before slowly experiencing a phase transition during which the field, extremely slowly, moves towards its zero temperature expectation value. We show that it is possible to obtain enough e-folds of expansion as well as the correct spectrum of perturbations without hugely fine-tuned parameters in the potential (albeit with many spectator fields). We also comment on how initial conditions for inflation can arise naturally in this situation. This chapter is based on the work published in [40]. • In chapter 3, we study the (▇▇▇▇▇-▇▇▇▇▇▇▇-)▇▇▇▇▇ quartic coupling which be- comes negative at high energies rendering our current electroweak vacuum metastable, but with an instability timescale much longer than the age of the current universe. During cosmological inflation, unless there is a non-minimal coupling to gravity, the ▇▇▇▇▇ field is pushed away from the origin of its po- tential due to quantum fluctuations. It is therefore a mystery how we have remained in our current vacuum if we went through such a period of inflation. In this chapter, we study the effect of top quarks created gravitationally during inflation and their effect upon the ▇▇▇▇▇ potential using only general relativity with minimal couplings and Standard Model particle physics. We show how the evolution of the ▇▇▇▇▇ field during inflation is modified concluding that this effect is non-negligible for scales of inflation close to or larger than the stability scale but small for scales where the ▇▇▇▇▇ is stable. Also, we briefly discuss the effect of other fermions on the ▇▇▇▇▇ instability. This chapter is based on work published in [41]. Chapter 2
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