Alternative quantization of the Hamiltonian in isotropic loop quantum cosmology

Details Alternative quantization of the Hamiltonian in isotropic loop quantum cosmology Alternative quantization of the Hamiltonian in isotropic loop quantum cosmology

2009-02-11

arxiv.org/abs/0902.1913v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, 2 figures; a few modifications, references added

Scientific paper

Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and effective scenario, are robust against the ambiguities. In this paper, we consider a typical quantization ambiguity arising from the quantization of the field strength of the gravitational connection. An alternative Hamiltonian constraint operator is constructed, which is shown to have the correct classical limit by the semiclassical analysis. The effective Hamiltonian incorporating higher order quantum corrections is also obtained. In the spatially flat FRW model with a massless scalar field, the classical big bang is again replaced by a quantum bounce. Moreover, there are still great possibilities for the expanding universe to recollapse due to the quantum gravity effect. Thus, these key features are robust against this quantization ambiguity.

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