Chapter 1 Introduction Cosmological Inflation is a leading candidate for the solution of the three main problems of the standard Big Bang scenario: the Horizon, Flatness and Relic problems. It also has the ability to seed the initial conditions required to explain the observed large-scale structure of the Universe. (For a textbook on this topic, see [1].) In the simplest scenario, quantum fluctuations of a scalar field are converted to classical perturbations around the time of horizon exit, after which they become frozen. This gives rise to the primordial curvature perturbation, ζ , which grows under the influence of gravity to give rise to all of the large-scale structure in the Universe. The observed value of the spectrum of the primordial curvature perturbation is P 1 2 ζ ( k$_{0}$ ) ∼ 10 − $^{5}$. Moving away from this simplest scenario, there has been much work done on trying to generate the observed ζ in other scenarios, such as the curvaton [2–23], inhomogeneous reheating [4,19–22,24–30], “end of inflation” [13,30– 36] (also see [37]) and inhomogeneous phase transition [38]. (Also see [39].) This thesis is structured as follows. In Chapter 2 we talk about the 1