The Dapor–Liegener model of loop quantum cosmology: a dynamical analysis

The Dapor–Liegener model of loop quantum cosmology (LQC), which depicts an emergent universe from a de Sitter regime in the contracting phase is studied from the mathematical viewpoint of dynamical systems and compared with the standard model of LQC. Dealing with perturbations, on the contrary to standard LQC where at early times all the scales are inside the Hubble radius, we show that it is impossible to implement the matter bounce scenario due to the fact that an emergent de Sitter regime in the contracting phase implies that all the scales are outside of the Hubble radius in a past epoch