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

The self-adjointness of an evolution operator Theta(Lambda) 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 Lambda > 0. It is shown that, for Lambda < Lambda(c) approximate to 10.3l(Pl)(-2), the operator admits many self-adjoint extensions, each of the purely discrete spectrum. On the other hand for Lambda >= Lambda(c) the operator is essentially self-adjoint, however the physical Hilbert space of the model does not contain any physically interesting states.