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- relative amounts of Hydrogen, Helium and Deuterium
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Please elaborate. You sound like you've started off on a great foot, but why do those ratios matter? What is the significance?
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galaxies look the different (younger) the further out you look
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Please elaborate on what you mean by "look younger." I wonder how you know what a "young" galaxy looks like, as opposed to an "old" galaxy.
For whatever hypothesis you propose for differentiating when a galaxy is "old" versus "young"
What experiment do I conduct to try to disprove any or all of that hypothesis? What apparatus would I build? What would the experiment entail? How would I tell my results have disproved the hypothesis?
What prediction could I make about something people have yet to observe? That is, what could we do to check that hypothesis' predictions? Does it even make predictions that are checkable? If so, what are they, or what is one of them?
Also, please describe how you know how "far out" galaxies are. You didn't send a space ship with a tape measure after all.
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In addition (though I'm not sure this counts as a prediction), the age of the universe derived from CMB agrees with other methods of estimation.
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I'm not sure either. What are those other estimations? What is the content of them?
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So, what further tests/experiments?
Well, a few ideas :
- we've no idea what Dark Matter / Dark Energy are, so it's possible as we learn more about them that they could support or destroy the model (eg. making it impossible for galaxies to form).
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I don't have any idea what dark matter or energy are either. I wonder by what mechanism things I nor you have any knowledge about could support or destroy a model. Please elaborate.
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- The Large Hadron Collider has been built specifically to examine behaviour at temperatures/pressures not seen since the BB. The behaviour observed could affect the model.
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What behavior, theoretical or not, do you refer to? How would it "support" a model?
Might I say as an aside, I'm all for smashing things together at high speeds; regardless of the pure scientific discovery that might come of it.
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Bottom line, BB is still a falsifiable theory, but it's up to the supporters of other models to make predictions that better match observations before people will switch 
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Why?