
University of Helsinki, Helsinki 2006 NonGaussian Cosmological Perturbations from Hybrid Inflation and PreheatingAntti VäihkönenDoctoral dissertation, March 2006. This thesis consists of four research papers and an introduction providing some background. The structure in the universe is generally considered to originate from quantum fluctuations in the very early universe. The standard lore of cosmology states that the primordial perturbations are almost scaleinvariant, adiabatic, and Gaussian. A snapshot of the structure from the time when the universe became transparent can be seen in the cosmic microwave background (CMB). For a long time mainly the power spectrum of the CMB temperature fluctuations has been used to obtain observational constraints, especially on deviations from scaleinvariance and pure adiabacity. NonGaussian perturbations provide a novel and very promising way to test theoretical predictions. They probe beyond the power spectrum, or two point correlator, since nonGaussianity involves higher order statistics. The thesis concentrates on the nonGaussian perturbations arising in several situations involving two scalar fields, namely, hybrid inflation and various forms of preheating. First we go through some basic concepts  such as the cosmological inflation, reheating and preheating, and the role of scalar fields during inflation  which are necessary for the understanding of the research papers. We also review the standard linear cosmological perturbation theory. The second order perturbation theory formalism for two scalar fields is developed. We explain what is meant by nonGaussian perturbations, and discuss some difficulties in parametrisation and observation. In particular, we concentrate on the nonlinearity parameter. The prospects of observing nonGaussianity are briefly discussed. We apply the formalism and calculate the evolution of the second order curvature perturbation during hybrid inflation. We estimate the amount of nonGaussianity in the model and find that there is a possibility for an observational effect. The nonGaussianity arising in preheating is also studied. We find that the level produced by the simplest model of instant preheating is insignificant, whereas standard preheating with parametric resonance as well as tachyonic preheating are prone to easily saturate and even exceed the observational limits. We also mention other approaches to the study of primordial nonGaussianities, which differ from the perturbation theory method chosen in the thesis work. The title page of the publication
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