Bouncing Universe in loop quantum gravity: full theory calculation

In loop quantum gravity mathematically rigorous models of full quantum gravity were proposed. In this paper we will 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 our homogeneous-isotropic model to the spatially flat sector. After this restriction the number of degrees of freedom gets substantially reduced. This allows us to make numerical and analytical 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.