Loop quantum cosmology evolution operator of an FRWuniverse with a positive cosmological constant

Abstract

The self-adjointness of an evolution operator Θ corresponding to the model of the flat FRW universe with massless scalar field and cosmological constant quantized in the framework of loop quantum cosmology is studied in the case > 0. It is shown that, for < c 10:3‘ 2Pl , the operator admits many self-adjoint extensions, each of the purely discrete spectrum. On the other hand for c the operator is essentially self-adjoint, however the physical Hilbert space of the model does not contain any physically interesting states.