Instabilities and nonlinear interactions of scalar field perturbations in models of cosmological inflation

The theory of cosmological inflation, despite being widely accepted as the important ingredient of the concordance model of cosmology, suffers from a number of drawbacks and unresolved issues. In particular, it is still a very general concept and the relation of the inflaton field or fields with the standard model of particle physics remains unclear. Further theoretical inquiry, as well as improved measurements of cosmological parameters are needed to verify which, if any, model of inflation is realized in Nature. The results of our research presented herein are aimed at decreasing the uncertainty of interpretation of CMB observables with respect to the features of inflationary models by improving the knowledge about post-inflationary reheating era and checking the impact of geometrical destabilization of inflation on inflationary trajectory. This goal was realized through three distinct research objectives. The first one was the investigation of the plausibility of the self-resonance mechanism as reheating scenario in single-field inflationary models. Our investigation showed that self-resonance reheating is very rare among inflationary models. Out of 52 models, which we investigated, barring the already known example of single-field α-attractors T-models, we selected only one - KKLT inflationary model - characterized by effective parametric resonance reheating. The second objective of our research was the analysis of parametric resonance reheating in α-attractor T-models of inflation. We showed that near the end of inflation the initially stable second field present in these models become tachyonic and is destabilized. We found that taking this fact into account may strongly speed up reheating compared to the previous speculations, which we based on the single field approximations. For small values of the parameter α reheating can be almost instantaneous and complete within the fraction of an e-fold. The third research objective was the analysis how the mechanism of geometric destabilization may affect the inflationary trajectory. If we treat inflation as an effective field theory this mechanism emerge very naturally and seems to be quite generic. We found that it can significantly change the inflationary trajectory and results in the prolonged period of inflation. In this way the geometrical destabilization may change the cosmological predictions of the inflationary models