Do sewn up singularities falsify the Palatini cosmology?

Marek Szydłowski; Aleksander Stachowski; Andrzej Borowiec; Aneta Wojnar

doi:10.1140/epjc/s10052-016-4426-9

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2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2016) 76: 567
https://doi.org/10.1140/epjc/s10052-016-4426-9

Regular Article - Theoretical Physics

Do sewn up singularities falsify the Palatini cosmology?

Marek Szydłowski¹^,2^*, Aleksander Stachowski¹, Andrzej Borowiec³ and Aneta Wojnar³^,4

¹ Astronomical Observatory, Jagiellonian University, Orla 171, 30-244, Kraków, Poland
² Mark Kac Complex Systems Research Centre, Jagiellonian University, ul. Łojasiewicza 11, 30-348, Kraków, Poland
³ Institute for Theoretical Physics, University of Wrocław, pl. M. Borna 9, 50-204, Wrocław, Poland
⁴ Dipartimento di Fisica, Universita di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Via Cinthia, 9, 80126, Naples, Italy

^* e-mail: marek.szydlowski@uj.edu.pl

Received: 30 April 2016
Accepted: 10 October 2016
Published online: 21 October 2016

Abstract

We investigate further (cf. Borowiec et al. JCAP 1601(01):040, 2016) the Starobinsky cosmological model $R+\gamma R^2$ 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 $\gamma$ is, in this case, a generic feature of the early evolution of the universe. It is demonstrated that $\gamma$ equal zero is a bifurcation parameter and the dynamics qualitatively changes as the $\gamma$ sign is changing. On the other side for the case of negative $\gamma$ 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 $\Omega _{\gamma } > 0$ is favored by data only very small values of $\Omega _{\gamma }$ parameter are allowed if we require agreement with the $\Lambda$ CDM model. From the statistical analysis of astronomical observations, we deduce that the case of only very small negative values of $\Omega _\gamma$ cannot be rejected. Therefore, observation data favor the universe without the ghost states ( $f'(\hat{R})>0$ ) and tachyons ( $f''(\hat{R})>0$ ).