  We construct a noncommutative extension of the Loop Quantum Cosmology
effective scheme for the open FLRW model with a free scalar field via a theta
deformation. Firstly, a deformation is implemented in the configuration sector,
among the holonomy variable and the matter degree of freedom. We show that this
type of noncommutativity retain, to some degree, key features of the Loop
Quantum Cosmology paradigm for a free field. Secondly, a deformation is
implemented in the momentum sector, among the momentum associated to the
holonomy variable and the momentum associated to the matter field. We show that
in this latter case the scalar field energy density is bounded and has the same
maximum as in standard Loop Quantum Cosmology, signaling a higher degree of
compatibility.
