Effective dynamics of the closed loop quantum cosmology
  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 $\Lambda_{\text{c}} =\frac{\sqrt{3}m^2_{\text{Pl}}}{2\pi\gamma^3} \simeq
21 m^2_{\text{Pl}}$ 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.
