Second-order cosmological perturbations in two-field inflation and predictions for non-Gaussianity

TL;DR

This paper investigates second-order cosmological perturbations in two-field inflation models to predict non-Gaussianity, providing analytical and numerical insights into how field interactions influence observable non-Gaussian signals.

Contribution

It derives the second-order gauge-invariant perturbation forms and a formula for non-Gaussianity parameter fNL in two-field inflation models, advancing understanding of non-linear effects.

Findings

Analytical expression for fNL as a function of potential and field trajectory.

Numerical verification of the analytical results within the slow-roll approximation.

Insights into how isocurvature perturbations affect non-Gaussianity magnitude.

Abstract

Inflationary predictions for the power spectrum of the curvature perturbation have been verified to an excellent degree, leaving many models compatible with observations. In this thesis we studied third-order correlations, that might allow one to further distinguish between inflationary models. From all the possible extensions of the standard inflationary model, we chose to study two-field models with canonical kinetic terms and flat field space. The new feature is the presence of the so-called isocurvature perturbation. Its interplay with the adiabatic perturbation outside the horizon gives birth to non-linearities characteristic of multiple-field models. In this context, we established the second-order gauge-invariant form of the adiabatic and isocurvature perturbation and found the third-order action that describes their interactions. Furthermore, we built on and elaborated the long-wavelength formalism in order to acquire an expression for the parameter of non-Gaussianity fNL as a function of the potential of the fields. We next used this formula to study analytically, within the slow-roll hypothesis, general classes of potentials and verified our results numerically for the exact theory. From this study, we deduced general conclusions about the properties of fNL, its magnitude depending on the characteristics of the field trajectory and the isocurvature component, as well as its dependence on the magnitude and relative size of the three momenta of which the three-point correlator is a function.