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

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 $a(t)$). In many of these works the speed of light $c$ is not addressed or is taken as constant (see for example the Dirac large number hypothesis, \cite{Dirac}). The same can be said of many works that assume the speed of light $c$ to vary with cosmological time $t$ or $a(t)$ (see for example \cite{ MaMo}). Again in many of these works the gravitational constant $G$ is not addressed or is taken as constant. We have two important remarks on these assumptions.