A recent short article in Physics Letters B (Ahmed Farag Ali and Saurya Dasc, "Cosmology from quantum potential") describes a quantum tweak to General Relativity that gives an interesting cosmological model: there is still a Big Bang, but there is no initial singularity. In other words, there is no beginning. The universe was always there, and always will be there. But most of the time, it is in a rather quiescent state, a quantum potential. Some time back, this quantum potential collapsed into a hot dense state -- not a singularity, just a hot dense state -- which produced the Big Bang. The model also predicts a cosmological constant with the correct value and provides a mechanism for dark energy to accelerate the expansion of the universe.
This model is not detailed -- it is what physicists call a semi-classical approximation, in which a few simple quantum ideas are added to a classical model: in this case, the Raychaudhuri equation, which is derived from General Relativity. The Raychaudhuri equation is used in the proof of the Penrose-Hawking singularity theorems that imply the existence of a singularity in the past of the universe in the usual cosmological models. But the quantum corrected Raychaudhuri equation (QRE) used by the authors of the letter does not predict such a singularity in the universe's past.
In summary, we have shown here that as for the QRE, the second order Friedmann equation derived from the QRE also contains two quantum correction terms. These terms are generic and unavoidable and follow naturally in a quantum mechanical description of our universe. Of these, the first can be interpreted as cosmological constant or dark energy of the correct (observed) magnitude and a small mass of the graviton (or axion). The second quantum correction term pushes back the time singularity indefinitely, and predicts an everlasting universe. While inhomogeneous or anisotropic perturbations are not expected to significantly affect these results, it would be useful to redo the current study with such small perturbations to rigorously confirm that this is indeed the case. Also, as noted in the introduction, we assume it to follow general relativity, whereas the Einstein equations may themselves undergo quantum corrections, especially at early epochs, further affecting predictions. Given the robust set of starting assumptions, we expect our main results to continue to hold even if and when a fully satisfactory theory of quantum gravity is formulated. For the cosmological constant problem at late times on the other hand, quantum gravity effects are practically absent and can be safely ignored. We hope to report on these and related issues elsewhere.