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An open FRW model in loop quantum cosmology

Łukasz Szulc

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An open FRW model in loop quantum cosmology is considered. The left and right invariant vector fields and holonomies along them are studied. It is shown that in the hyperbolic geometry of k = −1 it is possible to construct a suitable loop which provides us with the quantum scalar constraint originally introduced by Vandersloot [19]. The quantum scalar constraint operator with negative cosmological constant is proved to be essentially self-adjoint.


PACS

98.80.Qc Quantum cosmology

98.80.Cq Particle-theory and field-theory models of the early Universe (including cosmic pancakes, cosmic strings, chaotic phenomena, inflationary universe, etc.)

95.30.Sf Relativity and gravitation

04.60.Pp Loop quantum gravity, quantum geometry, spin foams

MSC

85A40 Cosmology (For relativistic cosmology, see 83F05)

83C45 Quantization of the gravitational field

83F05 Cosmology

57R25 Vector fields, frame fields

51M10 Hyperbolic and elliptic geometries (general) and generalizations

Subjects

Gravitation and cosmology

Astrophysics and astroparticles

Dates

Issue 24 (21 December 2007)

Received 13 July 2007, in final form 29 October 2007

Published 27 November 2007



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