Two restrictions in the theories that include $G(t)$ and $c(t)$ varying with time

TL;DR

This paper discusses the theoretical implications of allowing both the gravitational constant G(t) and the speed of light c(t) to vary over time, under the restriction that their combination remains constant, impacting cosmological models.

Contribution

It introduces two key restrictions on theories where G and c vary with time, specifically maintaining the constancy of 8πG/c^4, which influences cosmological dynamics.

Findings

The restriction 8πG/c^4 = constant is significant for varying G and c theories.

Varying G and c with this restriction affects cosmological equations.

The paper provides theoretical insights into the consistency of such varying constants.

Abstract

Much work has been done taking into account the possibility that the gravitational {\it constant} $G$ may vary with cosmological time $t$ (or with the cosmological scale factor $a(t)$). The same may be said about the speed of light $c$. We present here two important remarks on these subject. These remarks include $G(t)$ and $c(t)$ varying with time with the restriction $8 \pi G / c^4 = \hbox{constant}$