  This article presents the lattice-smeared gravity phase space reduction
defined by the cosmological gauge-fixing conditions. These conditions are
specified to reduce the SU(2) symmetry and the spatial diffeomorphism
invariance of the loop quantum gravity's Fock space, known as the spin network.
The internal symmetry is fixed to the Abelian case and the diffeomorphism
invariance is simultaneously reduced to spatial translations. By rigorously
satisfying the reduced gauge symmetries, the resulting cosmological model is
precisely the limit of the gravitational theory expressed in terms of
holonomies and fluxes. Moreover, the obtained Hamiltonian constraint is finite
(without any cut-off introduction) and exact (without the holonomy expansion
around short links). Furthermore, it has the form of the sum over elementary
cuboidal cells. Finally, the simple structure of its homogeneities and
anisotropies should allow to describe the quantum cosmological evolution of the
Universe in terms of transition amplitudes, instead of using perturbative
approximations.
