Do sewn up singularities falsify the Palatini cosmology?

Abstract

We investigate further (cf. Borowiec et al. JCAP 1601(01):040, 2016) the Starobinsky cosmological model R+ γR2 in the Palatini formalism with a Chaplygin gas and baryonic matter as a source in the context of singularities. The dynamics reduces to the 2D sewn dynamical system of a Newtonian type (a piece-wise-smooth dynamical system). We demonstrate that the presence of a sewn up freeze singularity (glued freeze type singularities) for the positive γ is, in this case, a generic feature of the early evolution of the universe. It is demonstrated that γ equal zero is a bifurcation parameter and the dynamics qualitatively changes as the γ sign is changing. On the other side for the case of negative γ instead of the big bang the sudden bounce singularity of a finite scale factor does appear and there is a generic class of bouncing solutions. While the Ω γ> 0 is favored by data only very small values of Ω γ parameter are allowed if we require agreement with the Λ CDM model. From the statistical analysis of astronomical observations, we deduce that the case of only very small negative values of Ω γ cannot be rejected. Therefore, observation data favor the universe without the ghost states (f′(R^) > 0) and tachyons (f′ ′(R^) > 0).