Effects of the quantisation ambiguities on the Big Bounce dynamics

Abstract

In this paper we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator $\hat{F}$ and result in different forms of the effective Hamiltonian. Such an ambiguity of the choice of this expression from some class of functions is allowed in the framework of loop quantisation. Our main goal is to show how such modifications can influence the bouncing universe scenario in the loop quantum cosmology. In effective models considered we classify all evolutional paths for all admissible initial conditions. The dynamics is reduced to the form of a dynamical system of the Newtonian type on a 2-dimensional phase plane. These models are equivalent dynamically to the FRW models with the decaying effective cosmological term parametrised by the canonical variable $p$ (or by the scale factor $a$). We find that for the positive cosmological constant there is a class of oscillating models without the initial and final singularities. The new phenomenon is the appearance of curvature singularities for the finite values of the scale factor, but we find that for the positive cosmological constant these singularities can be avoided. For the positive cosmological constant the evolution begins at the asymptotic state in the past represented by the deSitter contracting (deS${}_{-}$) spacetime or the static Einstein universe H=0 or $H=-\infty$ state and reaches the deSitter expanding state (deS${}_{+}$), the state H=0 or $H=+\infty$ state. In the case of the negative cosmological constant we obtain the past and future asymptotic states as the Einstein static universes.

RevTeX4, 28 pages, 11 figs; rev.2 new section on exact solutions; (v3) published version

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Cited by in corpus (12)

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• Turning Big Bang into Big Bounce: I. Classical Dynamics
• New Hamiltonians for loop quantum cosmology with arbitrary spin representations
• Loop quantum cosmology with higher order holonomy corrections
• Do sewn singularities falsify the Palatini cosmology?
• Anomaly free cosmological perturbations with generalised holonomy correction in loop quantum cosmology
• Effective dynamics of the closed loop quantum cosmology
• Cosmological implications of generalized holonomy corrections
• Gravitational waves with generalized holonomy corrections
• Asymmetric cyclic evolution in polymerised cosmology
• Covariant single-field formulation of effective cosmological bounces
• Examination of the nature of the Bianchi type cosmological singularities