Effective dynamics of the closed loop quantum cosmology

Abstract

In this paper we study dynamics of the closed FRW model with holonomy corrections coming from loop quantum cosmology. We consider models with a scalar field and cosmological constant. In case of the models with cosmological constant and free scalar field, dynamics reduce to 2D system and analysis of solutions simplify. If only free scalar field is included then universe undergoes non-singular oscillations. For the model with cosmological constant, different behaviours are obtained depending on the value of $\Lambda$. If the value of $\Lambda$ is sufficiently small, bouncing solutions with asymptotic de Sitter stages are obtained. However if the value of $\Lambda$ exceeds critical value ${\Lambda }_{\text{c}}=\frac{\sqrt{3}{m}_{\text{Pl}}^2}{2\pi {\gamma }^3}\simeq 21m_{\text{Pl}}^2$ then solutions become oscillatory. Subsequently we study models with a massive scalar field. We find that this model possess generic inflationary attractors. In particular field, initially situated in the bottom of the potential, is driven up during the phase of quantum bounce. This subsequently leads to the phase of inflation. Finally we find that, comparing with the flat case, effects of curvature do not change qualitatively dynamics close to the phase of bounce. Possible effects of inverse volume corrections are also briefly discussed.

18 pages, 11 figures

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• Application of higher order holonomy corrections to perturbation theory of cosmology
• Loop Quantum Cosmology Scalar Field Models
• Mimetic gravity: mimicking the dynamics of the primeval universe in the context of loop quantum cosmology
• Alternative $k=-1$ loop quantum cosmology
• Effective LQC model for k=+1 isotropic cosmologies from spatial discretisations
• Asymmetric cyclic evolution in polymerised cosmology