  We study models where the gauge coupling constants, masses and the
gravitational constant are functions of some conserved charge in the universe,
and furthermore a cosmological constant that depends on the total charge of the
universe. We first consider the standard Dirac action, but where the mass and
the electromagnetic coupling constant are a function of the charge in the
universe and afterwards extend this to curved spacetime and consider gauge
coupling constants, the gravitation constant and the mass as a function of the
charge of the universe, which represent a sort of Mach principle for all the
constants of nature. In the flat space formulation, the formalism is not
manifestly Lorentz invariant, however Lorentz invariance can be restored by
performing a phase transformation of the Dirac field, while in the curved space
time formulation, there is the additional feature that some of the equations of
motion break the general coordinate invariance also, but in a way that can be
understood as a coordinate choice only, so the equations are still of the
General Relativity type, but with a certain natural coordinate choice, where
there is no current of the charge. We have generalized what we have done and
also constructed a cosmological constant which depends on the total charge of
the universe. If we were to use some only approximately conserved charge for
these constructions, like say baryon number (in the context of the standard
model), this will lead to corresponding violations of Lorentz symmetry in the
early universe for example. The construction of charge dependent contributions
can also be motivated from the structure of the "infra-red counter terms"
needed to cancel infra red divergences for example in three dimensions.
