Novel techniques for calculating in ationary observables
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Comparing the predictions from different inflation models to observations of the Cosmic Microwave Background (CMB) and the Large-Scale Structure (LSS) is a non-trivial task. One needs to calculate the statistics of the primordial curvature perturbation, ζ, to be able to compare to observational constraints. There exist many formalisms for such calculations, each with its own benefits and drawbacks, depending on the inflation model being considered. One popular method, the δN formalism, calculates the evolution of the statistics of ζ on superhorizon scales. δN assumes that the number of e-folds as a function of the scalar fields present in the model, N, is Taylor-expandable and that the Taylor series converges sufficiently fast. Unfortunately, this assumption breaks down in some cases. As a solution, in this thesis, we first extend the standard δN formalism so that it can be applied to any arbitrary function of N, irrespective of whether the N function is Taylor-expandable or not. We test the validity of the formalism on a pre-generated N function from a realistic model and find that the method shows marked improvement over regular δN. This extension of δN, which we call ‘non-perturbative δN’, involves integrating the N function against a probability distribution function for the fields. When the N function is highly featured, a convenient method to perform the calculations is Monte Carlo integration. As an example, in the last part of the thesis we study massless preheating. We run our own lattice simulations and implement the non-perturbative expressions in a Monte Carlo fashion. Doing so, we calculate accurately the two- and three-point functions of ζ in this model for the first time.
- Theses