Limiting curvature mimetic gravity for group field theory condensates

Nonsingular bouncing cosmologies are realized in limiting curvature mimetic gravity by means of a multivalued potential f(□φ) depending on the d'Alembertian of a scalar field φ. We determine the functional form of such a potential so as to exactly reproduce the cosmological background dynamics obtained in the group field theory approach to quantum gravity. The original proposal made by Chamseddine and Mukhanov [J. Cosmol. Astropart. Phys. 03 (2017) 009JCAPBP1475-751610.1088/1475-7516/2017/03/009], which was shown to lead to a background dynamics reproducing the effective dynamics of loop quantum cosmology, is here recovered as a particular case for some specific choices of the parameters of our model. We also clarify some issues related to the multivaluedness of the function f, showing in particular that its functional form can be unambiguously reconstructed by imposing appropriate matching conditions at the branching points.