Limiting curvature mimetic gravity and its relation to Loop Quantum Cosmology

Abstract

Considering as usual that the underlying geometry of our universe is well described by the spatially flat Friedmann–Lemaître–Robertson–Walker line element, we review how the background of holonomy corrected Loop Quantum Cosmology (LQC) could be obtained as a simple modified version of the mimetic gravity. We also analyze the scalar and tensor perturbations of this modified mimetic model, from which we find that at the level of tensor perturbations it is indistinguishable from General Relativity while at the level of scalar perturbations, the modified mimetic model, which has the same background as LQC, does not exhibit the same properties as LQC in the so-called deformed algebra approach