We present a flat (K=0) cosmological model, described by a perfect fluid with
the ``constants'' G,c and Λ varying with cosmological time t. We
introduce Planck\'s ``constant'' ℏ in the field equations through the
equation of state for the energy density of radiation. We then determine the
behaviour of the ``constants'' by using the zero divergence of the second
member of the modified Einstein\'s field equations i.e.
div(c4GTij+δijΛ)=0, together with the
equation of state and the Einstein cosmological equations. Assuming realistic
physical and mathematical conditions we obtain a consistent result with ℏc=constant. In this way we obtain gauge invariance for the Schr\"{o}dinger
equation and the behaviour of the remaining ``constants''Comment: 15 pages, RevTeX