Gravitational coupling, dynamical changes of units and the cosmological constant problem

A spacetime interval connecting two neighbouring points can be measured in different unit systems. For instance, it can be measured in atomic unit defined in terms of fundamental constants existing in quantum theories. It is also possible to use a gravitational unit which is defined by the use of properties of macroscopic objects. These two unit systems are usually regarded as indistinguishable up to a constant conversion factor. Here we consider the possibility that these two units are related by an epoch-dependent conversion factor. This is a dynamical changes of units. Regarding a conformal transformation as a local unit transformation, we use a gravitational model in which the gravitational and the matter sectors are given in different conformal frames (or unit systems). It is relevant to the cosmological constant problem, namely the huge discrepancy between the estimated and the observational values of the cosmological constant in particle physics and cosmology, respectively. We argue that the problem arises when one ignores evolution of the conversion factor relating the two units during expansion of the Universe. Connection of the model with violation of equivalence principle and possible variation of fundamental constants are also discussed. (paper)