How do we know that spacetime is expanding

[Gerinski]

What are the facts by which we believe that it's spacetime itself which is expanding since the big bang and not that it's only the matter-energy in the universe which expands in a pre-existing unchanging spacetime canvas?

 

[S.Vasojevic]

What are the facts by which we believe that it's spacetime itself which is expanding since the big bang and not that it's only the matter-energy in the universe which expands in a pre-existing unchanging spacetime canvas?

There is no 'pre-existing spacetime canvas'. Space and time are not some 'outside entities', they are just notions to describe things in our universe. There is no space and time where 'there is no universe'.

Other than that, you may find some answers to your question here: https://www.physicsforums.com/showthread.php?t=283237"

 

[Wallace]

What are the facts by which we believe that it's spacetime itself which is expanding since the big bang and not that it's only the matter-energy in the universe which expands in a pre-existing unchanging spacetime canvas?

I'd recommend you read the thread S.Vasojevic linked to, I make some detailed comments in that.

In brief, the 'expanding universe' refers to the fact that the stuff in the universe is moving away from all the other stuff in the universe. Describing this as 'space-time expanding' is a very useful mathematical construct, but it is the motion of the material that is important.

So the error is that it is not believed that 'space-time itself is expanding', at least in reference to the way professional cosmologists go about their work. This notion is a common misunderstanding of the co-ordinate system that cosmologists use to conveniantly do calculations in an expanding universe. It is not a physical theory or statement of some physical reality.