https://iopscience.iop.org/article/10.3847/1538-4357/aae5f7/... says:

> On the other hand,during the past 2 decades great attention has been paid to the theories with varying speed of light (VSL), in which the speed of light might be dynamical and could have been varying in the past. ...

> The measurement of c in the distant universe is an almost completely uncharted territory. Recently, with the angular diameter distances measured for intermediate-luminosity quasars extending to high redshifts, Cao et al.(2017a) performed the first measurement of the speed of light referring to the redshift baseline z = 1.70. The result was in very good agreement with the value of c obtained on Earth(i.e.,at z = 0).

> “It is worth recalling that Ellis & Uzan (2005) gave a sobering review of serious conceptual problems one faces while trying to change the status of c in physics. In particular, they stressed that it is usually not consistent to allow a constant to vary in an equation that has been derived from a variational principle under the hypothesis of this quantity being constant. Therefore, one needs to go back to the Lagrangian and derive new equations after having replaced the constant by a dynamical field.”

The math is a bit out of my depth...did they go back to the Lagrangian and derive new equations after having replaced the constant by a dynamical field?

People have at least once though the citation escapes me, it was 2006ish. And it could be found in agreement with observation. Not that I believe in it.

I missed this the first time - https://en.wikipedia.org/wiki/Variable_speed_of_light (I used Google Scholar to find that first reference).

There are about a dozen references in the 2006ish timeframe.