5 papers found.

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We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on noncommutative spaces are derived from a quantum Hodge star operator. This general noncommutative geometry construction is then exemplified in ...

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 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 ...

We study Yang-Baxter sigma models with deformed 4D Minkowski spacetimes arising from classical r-matrices associated with κ-deformations of the Poincaré algebra. These classical κ-Poincaré r-matrices describe three kinds of deformations: 1) the standard deformation, 2) the tachyonic deformation, and 3) the light-cone deformation. For each deformation, the metric and two-form ...