It was shown recently that replacing classical geodesics with quantal (Bohmian) trajectories gives
rise to a quantum corrected Raychaudhuri equation (QRE). Here we derive the second order Friedmann
equations from the QRE, and show that this also contains a couple of quantum correction
terms, the first of which can be interpreted as cosmological constant (and gives a correct estimate
of its observed value), or as dark matter, while the second as a radiation term in the early universe,
which gets rid of the big-bang singularity and predicts an infinite age of our universe.