A Theory of time-varying Constants

TL;DR

This paper develops a cosmological model with time-varying gravitational and cosmological constants, ensuring gauge invariance and consistent physical behavior by incorporating Planck's constant into Einstein's equations.

Contribution

It introduces a novel framework where G, c, and Λ vary with time while maintaining gauge invariance and physical consistency, linking quantum and cosmological constants.

Findings

Derived the behavior of varying constants consistent with Einstein's equations.

Established that  is constant, ensuring gauge invariance.

Provided a model compatible with physical and mathematical conditions.

Abstract

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'' $\hbar$ 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''