The abstract: In multi-field inflationary models coupling between field are not limited to the potential of the model, but can also be present in kinetic terms. In such a case it can be interpreted as a non-trivial structure of the space of fields. Non-vanishing curvature of this space can lead, if negative, to new phenomenon called geometrical destabilization. α-attractors are a very promising class of inflationary models. Their predictions for small values of α parameter are in remarkably good agreement with CMB data obtained by the Planck satellite. Since α-attractor models are by construction multi-field models, the dynamics of additional spectator field can play a role in the (p)reheating. When investigating the dynamics of two- field α-attractor T model, we have found that geometrical destabilization during (p)reheating leads to efficient fragmentation of the spectator field. As a result, the transition from the inflationary era to the radiation domination era is practically instantaneous and much faster than previously found in an effective theory including only the inflaton field. Recently, due to development of numerical software, we were able to overcome deficiencies of our primary analysis and got deeper insight into parametric dependence of the problem. Moreover, we estimated the spectrum of gravitational waves emitted during preheating in this model. The geometrical destabilization not necessarily happens after inflation; it can also can take place during inflationary epoch. One may suppose that it poses a threat to the successful inflation, as it may lead to its premature end. However, our studies have shown that this is not the case. The instability is shut down by the so called kinematic backreaction and the inflation proceeds further as a sidekicked inflation.

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