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We derive the Shafieloo, Hazra, Sahni and Starobinsky (SHSS) phenomenological formula for the radioactive-like decay of metastable dark energy directly from the principles of quantum mechanics. To this aim we use the Fock–Krylov theory of quantum unstable states. We obtain deeper insight on the decay process as having three basic phases: the phase of radioactive decay, the next ...

We consider FRW cosmology in \(f(R)= R+ \gamma R^2+\delta R^3\) modified framework. The Palatini approach reduces its dynamics to the simple generalization of Friedmann equation. Thus we study the dynamics in two-dimensional phase space with some details. After reformulation of the model in the Einstein frame, it reduces to the FRW cosmological model with a homogeneous scalar field ...

We classify singularities in FRW cosmologies, which dynamics can be reduced to the dynamical system of the Newtonian type. This classification is performed in terms of the geometry of a potential function if it has poles. At the sewn singularity, which is of a finite scale factor type, the singularity in the past meets the singularity in the future. We show that such singularities ...

We study cosmology with running dark energy. The energy density of dark energy is obtained from the quantum process of transition from the false vacuum state to the true vacuum state. We use the Breit–Wigner energy distribution function to model the quantum unstable systems and obtain the energy density of the dark energy parametrization \(\rho _\text {de}(t)\). We also use Krauss ...

Eur. Phys. J. C
Dynamical system approach to running cosmological models
**Aleksander** **Stachowski** 1
Marek Szydłowski 0 1
0 Mark Kac Complex Systems Research Centre, Jagiellonian University , Ł

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 ...