Gravitational field equations and the possibility of time variation of all masses

Recent developments in spontaneously broken gauge theories as well as in group analysis of cosmological models indicate that rest masses may change on the cosmological scale. Such an effect contradicts Einstein's equations of general relativity. The possibility of replacing Einstein's equations by the equations $R_{\mu \nu }=-4\mathrm{}\pi \kappa T_{\mu \nu }$ is explored. Cosmological models are calculated and time variation of all masses is derived for all isotropic, spatially homogeneous models. The result is $\frac{m°}{m}=-3H$, where $H$ is Hubble's constant. It is shown that the equations $R_{\mu \nu }=-4\mathrm{}\pi \kappa T_{\mu \nu }$ are not precluded by presently available observational and experimental data.