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@sveenoj.

The acceleration is measured by the redshift. We can see, the further away galaxys are the more their light turns red. See Doppler Effect/Redshift

"How can we be sure of that?"

We cant be 100% sure we can be relatively sure. In the distant past we had the same natural laws like today its safe to say those Supernovas couldnt shine more brightly.

Of course recently we saw that on huge scales natural forces (electromagnetism) seem to vary but afaik this doesnt change much in this case.