We illustrate a general reconstruction procedure for mimetic gravity. Focusing on abouncing cosmological background, we derive general properties that must be satisfied by thefunction f (f) implementing the limiting curvature hypothesis. We show how relevant physicalinformation can be extracted from power-law expansions of f in different regimes, correspondinge.g., to the very early universe or to late times. Our results are then applied to two specific modelsreproducing the cosmological

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... und dynamics obtained in group field theory and in loopquantum cosmology, and we discuss the possibility of using this framework as providing an effectivefield theory description of quantum gravity. We study the evolution of anisotropies near the bounce,and discuss instabilities of scalar perturbations. Furthermore, we provide two equivalent formulationsof mimetic gravity: one in terms of an effective fluid with exotic properties, the other featuring twodistinct time-varying gravitational "constants" in the cosmological equations.