  It has been known for some time that the cosmological Friedmann equation
deduced from General Relativity can be also obtained within the Newtonian
framework under certain assumptions. We use this result together with quantum
corrections to the Newtonian potentials to derive a set a of quantum corrected
Friedmann equations. We examine the behavior of the solutions of these modified
cosmological equations paying special attention to the sign of the quantum
corrections. We find different quantum effects crucially depending on this
sign. One such a solution displays a qualitative resemblance to other quantum
models like Loop Quantum Gravity or non-commutative geometry.
