Testing quantum effects of gravity and dark energy at laboratory scales

One of the biggest challenges in modern physics is how to unify gravity with quantum theory. The current understanding of gravity is based on the general theory of relativity (in the framework of classical physics). However, this description is incomplete as quantum mechanics is considered more fundamental. Although there are several different approaches to the problem of quantizing gravity, no fully consistent theory is yet to emerge. There is an absence of a complete quantum theory of gravity, and conventionally it is thought that the effects of quantum gravity occur only at high energies (Planck scale). Here we suggest that certain novel quantum effects of gravity can become significant even at lower energies and could be tested at laboratory scales. We also suggest a few indirect effects of dark energy that can show up at laboratory scales. Using these ideas, we set observational constraints on radio recombination lines of the Rydberg atoms. This could have consequences for atomic physics, especially for large n Rydberg atoms. We also set limits on the radio recombination lines of such atoms, which are consistent with observations. We further predict that the limit of the highest n for higher Z atoms will be higher, scaling as Z^(5⁄8). We further suggest that high-precision measurements of Casimir effects for smaller plate separation could also show some manifestations of the presence of dark energy.