  In Loop Quantum Gravity mathematically rigorous models of full quantum
gravity were proposed. In this paper we study a cosmological sector of one of
the models describing quantum gravity with positive cosmological constant
coupled to massless scalar field. In our previous research we introduced a
method to reduce the model to homogeneous-isotropic sector at the quantum
level. In this paper we propose a method to restrict to the spatially flat
sector. After this restriction the number of degrees of freedom gets
substantially reduced. This allows us to make numerical calculations.
Remarkably, the resulting model shares some structural similarities with the
Loop Quantum Cosmological models and therefore sheds some new light on the
relation between Loop Quantum Gravity and Loop Quantum Cosmology. According to
our model the evolution of the Universe is periodic. The quantum gravity
effects resolve the Big Bang singularity leading to a Big Bounce and cause the
Universe to contract after a classical expansion phase (Big Crunch).
