A Different Look at Dark Energy and the Time Variation of Fundamental Constants

This paper makes the simple observation that a fundamental length, or cutoff, in the context of Friedmann-Lema\^itre-Robertson-Walker (FRW) cosmology implies very different things than for a static universe. It is argued that it is reasonable to assume that this cutoff is implemented by fixing the number of quantum degrees of freedom per co-moving volume (as opposed to a Planck volume) and the relationship of the vacuum-energy of all of the fields in the theory to the cosmological constant (or dark energy) is re-examined. The restrictions that need to be satisfied by a generic theory to avoid conflicts with current experiments are discussed, and it is shown that in any theory satisfying these constraints knowing the difference between $w$ and minus one allows one to predict $\dot{w}$. It is argued that this is a robust result and if this prediction fails the idea of a fundamental cutoff of the type being discussed can be ruled out. Finally, it is observed that, within the context of a specific theory, a co-moving cutoff implies a predictable time variation of fundamental constants. This is accompanied by a general discussion of why this is so, what are the strongest phenomenological limits upon this predicted variation, and which limits are in tension with the idea of a co-moving cutoff. It is pointed out, however, that a careful comparison of the predicted time variation of fundamental constants is not possible without restricting to a particular model field-theory and that is not done in this paper.