Matilda111 said:
Do you think it would be worth looking into aspects of time dilation? Eg as the universe expands, time runs slower (and the time dilation slowly becomes more pronounced), this is looking into more general relativity. I could then compare supernovae, and how their luminosities decrease as a function of time. Or just compare lightcurves at different redshifts. Do you think I could go on to explain that if time is, in fact, slowing at a relative rate, then the speed of light could slow down?
I've been doing a heavy amount of research on this recently, and feel like I'm just going in circles.
Thank you very much for your help so far, it has been extremely useful :)
This subject is tough to research without the necessary background in relativity and cosmology. As
@Drakkith says, there is a well-known and thoroughly debunked "tired light" theory. Unfortunately, a number of pseudo-scientists still promote this, so you will find a lot online about it - including material that looks like genuine scientific material from respected sources.
The debunking of the tired light theory ultimately rests on the specific cosmological data, which fits a universal expansion, but not tired light.
As far as mainstream science is concerned the speed of light is now a defined constant and, along with the definition of the second, defines the metre. Also, it's a postulate of relativity that light travels at an invariant speed ##c##. Any analysis to the contrary must, in 2020, be an analysis of theories at odds with mainstream relativity and cosmology.
Given that we at PF focus on mainstream science, we probably can't help you much, I'm sorry to say. Also, as
@Dale said, any revision of mainstream theories would not result in a change to the speed of light, which is simply a conversion factor between units. Instead, it would focus on the fine structure constant, which is a dimensionless constant.
In summary, I think you need to be careful with this task, as you could easily be led astray into controversial preudo-science, some of which (I'm afraid) you've already picked up.