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We explore the physics of a Lagrangian fixed point within the framework of agravitational average effective action with scale-dependent couplings. Aconcrete model with a Lagrangian fixed point in four-dimensional space-time isformulated. The cosmological equations of this model are then solvedanalytically. The solution offers several non-trivial branches, which have thecharacteristics of a bouncing cosmology with late time inflation and variablegravitational couplings.

Bouncing cosmologies at the Lagrangian fixed point