Abstracts

Marek Szydlowski

Starobinsky cosmological model in Palatini formalism

We consider the Starobinsky model in the Palatini formalism in both Jordan and Einstein frames. The dynamic of models is also studied using dynamical system methods. From the phase portraits, one can find generic evolutionary scenarios of the evolution of the Universe. At each frame the topological structures of the phase space are different. In the Jordan frame, the sewn singularity appears which represents a finite scale factor type. Such singularity appears in the Starobinsky model in the Palatini formalism when dynamics is determined by the corresponding piecewise-smooth dynamical system. In the Einstein frame, in the Friedmann equation, dark energy is in the form of a scalar field with a potential whose the form is determined in a covariant way by the Ricci scalar of the FRW metric. In this frame, the energy density of matter and dark energy are also parameterized through the Ricci scalar and an interaction appears between matter and dark energy because the dark energy is decaying. In this model, during the cosmic evolution, the accelerating phase for the late times and the early inflation exist. These models in both frames are also analysed by statistical methods.