Problem with Surface Brightness & cosmological parameters

[ChrisVer]

I have a problem with some question I had to answer for the Surface Brightness \Sigma \propto \frac{Flux}{Angular~area}= \frac{F}{\Omega}.
I was able to show that \Sigma \propto (1+z)^{-4}
Then the question asks whether knowing its value for known candles or yardsticks, is a good way to determine the cosmological parameters...

I think that determining it will allow us to determine the redshift z and thus the scale factor a and its evolution. So we can know how a evolves and thus obtain the cosmological parameters from the Friedmann equations. Is that wrong?
However, somewhere I read that the dependence of (1+z)^{-4} is independent on the cosmological model ,something that made me think I was wrong... :(

Any idea?

 

[Chalnoth]

This may help:
http://arxiv.org/abs/astro-ph/9905116

 

[ChrisVer]

I have read this paper, unfortunately it doesn't give a clear answer (except for the ~(1+z)^-4 relationship I extracted) and the plots with different cosmological parameters models are done for the astrophysical distances and not surface brightness (independent of those distances)...

The last independence is making me confused...if it's independent on distances (and distances give Omegas) it shouldn't give any answer for Omegas... But then my question about the redshift $z$ is still annoying me :/

 

[Chalnoth]

I have read this paper, unfortunately it doesn't give a clear answer (except for the ~(1+z)^-4 relationship I extracted) and the plots with different cosmological parameters models are done for the astrophysical distances and not surface brightness (independent of those distances)...

The last independence is making me confused...if it's independent on distances (and distances give Omegas) it shouldn't give any answer for Omegas... But then my question about the redshift $z$ is still annoying me :/

Luminosity distance is the measure that is used for standard candles, angular diameter distance the measure for standard rulers.

Does that help any?