distant galaxies, the big bang and relativity

That makes a bit of sense - things looking bigger the farther away they are. I suppose if we were able to look all the way back to the Big Bang, it would have to appear everywhere in the sky.

If distant galaxies look bigger, do they appear brighter, as well?

Due to redshift depleting photon energies and spreading out photon arrival times too distant galaxies are much fainter than you would otherwise expect. If you happen to have googled angular diameter distance (which is defined to keep the usual way angular size varies with distance intact) there's an equivalent for this called luminosity distance (which keeps the 1/r^2 relation for brightness intact) you might see mentioned too.
 
Thank you :)

Before I proceed i'd like to ask you, to be patient wit my English - it is not my first language. And please don't hesitate to correct me if my grammar or wording is bad. Thank you.

First of all: I am not here to defend an opinion ot "theory". I just want to get a better understanding. So. if something whicht I write, sounds like an assertion, please understand it as a question. And I'd like to proceed to the next step in the discussion only if I am sure, that I have understood and that we agree in the present step :)

Let me start with what we know for sure.

We know, beyond any reasonable doubt, that the vacuum speed of light relative to its source is constant, no matter how fast the source of light moves. We also know this speed pretty exact (down to cm/second I think)
We also know the "signature" (absolute brightness an spectrum) of Type 1a supernovae from such explosions in "nearby" galaxies.
Furthermore we know, that our Universe is (still) expanding. We know that from the amount of red shift in the spectrum of distant stars and galaxies. And we can, at least roughly, estimate the distance of a supernova using it's relative brightness and the amount of red shift.

Is this so far correct?

Yes (although supernovae are not the only tool in a cosmologist's box - especially to measure continuing expansion in the nearby universe).
 
The first time I heard it explained, I heard that the red shift was caused by the distant galaxies moving away from us, but if I understand you correctly, the red shift is actually caused by the expansion of the universe. Or is it both?

The distinction is somewhere between zero and subtle at best and sometimes contentious at worst, but fortunately really only a matter of how best to explain it. They're kind of the same thing.

Sol wrote something on it here.

Light certainly continues to redshift as it travels through an expanding universe.
 

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