A Theory of time-varying Constants

We present a flat (K=0) cosmological model, described by a perfect fluid with the constants'' $G,c$ and $\Lambda$ varying with cosmological time $t$. We introduce Planck\'s constant’’ $\mathrm{\hslash }$ 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. $div(\frac{G}{c^{4}}T_{i}^{j}+\delta_{i}^{j}\Lambda)=0,$ together with the equation of state and the Einstein cosmological equations. Assuming realistic physical and mathematical conditions we obtain a consistent result with $\hbar c=constant$. In this way we obtain gauge invariance for the Schr\"{o}dinger equation and the behaviour of the remaining constants’’