Quantum-mechanical consequences of the Hubble expansion

Summary

Quantum-mechanical effects associated with a locally expanding space-time, described by a flat Robertson-Walker metric, are investigated. Specifically, we ask the following question: Can the local expansion rate of the Universe be detected by making precision measurements on atomic and molecular systems? A simple example involving a particle in an expanding box would seem to indicate that time-dependent fractional energy shifts may be detectable. Next, a careful perturbative analysis of realistic quantum-mechanical systems possessing quite generic smooth, continuous potentials is performed by employing an adiabatic approximation. It is found thatfor realistic systems the quantum effects due to a local spacetime expansion are too small to be detectable. Consequently, we also conclude that theactual physical size of an atomic or molecular system remains fairly constant, independent of the current rate of spatial expansion.